Expanding on the accepted answer, to apply this locally by applying a class to the outer modal div, you need to use the the modal-class property on the component rather than giving it a class like you would normally.

https://bootstrap-vue.org/docs/components/modal#variants

JS:

<b-modal modal-class="modal-fullscreen">
    ...
</b-modal>

CSS:

.modal-fullscreen .modal-dialog {
    max-width: 100%;
    margin: 0;
    top: 0;
    bottom: 0;
    left: 0;
    right: 0;
    height: 100vh;
    display: flex;
    position: fixed;
    z-index: 100000;
}

I've came up with a "responsive" solution for fullscreen modals:

Fullscreen Modals that can be enabled only on certain breakpoints. In this way the modal will display "normal" on wider (desktop) screens and fullscreen on smaller (tablet or mobile) screens, giving it the feeling of a native app.

Implemented for Bootstrap 3 and Bootstrap 4. Included by default in Bootstrap 5.

Bootstrap v5

Fullscreen modals are included by default in Bootstrap 5: https://getbootstrap.com/docs/5.0/components/modal/#fullscreen-modal

Bootstrap v4

The following generic code should work:

.modal {
  padding: 0 !important; // override inline padding-right added from js
}
.modal .modal-dialog {
  width: 100%;
  max-width: none;
  height: 100%;
  margin: 0;
}
.modal .modal-content {
  height: 100%;
  border: 0;
  border-radius: 0;
}
.modal .modal-body {
  overflow-y: auto;
}

By including the scss code below, it generates the following classes that need to be added to the .modal element:

+---------------------+---------+---------+---------+---------+---------+
|                     |   xs    |   sm    |   md    |   lg    |   xl    | 
|                     | <576px  | ≥576px  | ≥768px  | ≥992px  | ≥1200px |
+---------------------+---------+---------+---------+---------+---------+
|.modal-fullscreen    |  100%   | default | default | default | default | 
+---------------------+---------+---------+---------+---------+---------+
|.modal-fullscreen-sm |  100%   |  100%   | default | default | default | 
+---------------------+---------+---------+---------+---------+---------+
|.modal-fullscreen-md |  100%   |  100%   |  100%   | default | default |
+---------------------+---------+---------+---------+---------+---------+
|.modal-fullscreen-lg |  100%   |  100%   |  100%   |  100%   | default |
+---------------------+---------+---------+---------+---------+---------+
|.modal-fullscreen-xl |  100%   |  100%   |  100%   |  100%   |  100%   |
+---------------------+---------+---------+---------+---------+---------+

The scss code is:

@mixin modal-fullscreen() {
  padding: 0 !important; // override inline padding-right added from js

  .modal-dialog {
    width: 100%;
    max-width: none;
    height: 100%;
    margin: 0;
  }

  .modal-content {
    height: 100%;
    border: 0;
    border-radius: 0;
  }

  .modal-body {
    overflow-y: auto;
  }

}

@each $breakpoint in map-keys($grid-breakpoints) {
  @include media-breakpoint-down($breakpoint) {
    $infix: breakpoint-infix($breakpoint, $grid-breakpoints);

    .modal-fullscreen#{$infix} {
      @include modal-fullscreen();
    }
  }
}

Demo on Codepen: https://codepen.io/andreivictor/full/MWYNPBV/

Bootstrap v3

Based on previous responses to this topic (@Chris J, @kkarli), the following generic code should work:

.modal {
  padding: 0 !important; // override inline padding-right added from js
}

.modal .modal-dialog {
  width: 100%;
  height: 100%;
  margin: 0;
  padding: 0;
}

.modal .modal-content {
  height: auto;
  min-height: 100%;
  border: 0 none;
  border-radius: 0;
  box-shadow: none;
}

If you want to use responsive fullscreen modals, use the following classes that need to be added to .modal element:

• .modal-fullscreen-md-down - the modal is fullscreen for screens smaller than 1200px.
• .modal-fullscreen-sm-down - the modal is fullscreen for screens smaller than 922px.
• .modal-fullscreen-xs-down - the modal is fullscreen for screen smaller than 768px.

Take a look at the following code:

/* Extra small devices (less than 768px) */
@media (max-width: 767px) {
  .modal-fullscreen-xs-down {
    padding: 0 !important;
  }
  .modal-fullscreen-xs-down .modal-dialog {
    width: 100%;
    height: 100%;
    margin: 0;
    padding: 0;
  }
  .modal-fullscreen-xs-down .modal-content {
    height: auto;
    min-height: 100%;
    border: 0 none;
    border-radius: 0;
    box-shadow: none;
  } 
}

/* Small devices (less than 992px) */
@media (max-width: 991px) {
  .modal-fullscreen-sm-down {
    padding: 0 !important;
  }
  .modal-fullscreen-sm-down .modal-dialog {
    width: 100%;
    height: 100%;
    margin: 0;
    padding: 0;
  }
  .modal-fullscreen-sm-down .modal-content {
    height: auto;
    min-height: 100%;
    border: 0 none;
    border-radius: 0;
    box-shadow: none;
  }
}

/* Medium devices (less than 1200px) */
@media (max-width: 1199px) {
  .modal-fullscreen-md-down {
    padding: 0 !important;
  }
  .modal-fullscreen-md-down .modal-dialog {
    width: 100%;
    height: 100%;
    margin: 0;
    padding: 0;
  }
  .modal-fullscreen-md-down .modal-content {
    height: auto;
    min-height: 100%;
    border: 0 none;
    border-radius: 0;
    box-shadow: none;
  }
}

Demo is available on Codepen: https://codepen.io/andreivictor/full/KXNdoO.

Those who use Sass as a preprocessor can take advantage of the following mixin:

@mixin modal-fullscreen() {
  padding: 0 !important; // override inline padding-right added from js

  .modal-dialog {
    width: 100%;
    height: 100%;
    margin: 0;
    padding: 0;
  }

  .modal-content {
    height: auto;
    min-height: 100%;
    border: 0 none;
    border-radius: 0;
    box-shadow: none;
  }

}