Добавьте -ms-box-shadow к коду. Это может работать Box-Shadow, кажется, поддерживается в IE11.
.tb_records {
width:700px;
margin:50px auto;
border-collapse:collapse;
text-align:center;
}
.tb_records th, .tb_records td {
padding:15px;
border-bottom:1px solid #dddddd;
}
.tb_records tr {
-webkit-transition:box-shadow 0.5s linear;
-o-transition:box-shadow 0.5s linear;
-moz-transition:box-shadow 0.5s linear;
-ms-transition:box-shadow 0.5s linear;
transition:box-shadow 0.5s linear;
}
.tb_records tr:not(:first-child):hover {
-webkit-box-shadow:0 4px 8px 0 rgba(0, 0, 0, 0.2), 0 6px 20px 0 rgba(0, 0, 0, 0.19);
-moz-box-shadow:0 4px 8px 0 rgba(0, 0, 0, 0.2), 0 6px 20px 0 rgba(0, 0, 0, 0.19);
-ms-box-shadow:0 4px 8px 0 rgba(0, 0, 0, 0.2), 0 6px 20px 0 rgba(0, 0, 0, 0.19);
box-shadow:0 4px 8px 0 rgba(0, 0, 0, 0.2), 0 6px 20px 0 rgba(0, 0, 0, 0.19);
}
.tb_records tr td:first-child {
border-left:3px solid #FFFFFF;
-webkit-transition:border-left 0.3s linear;
-o-transition:border-left 0.3s linear;
-moz-transition:border-left 0.3s linear;
transition:border-left 0.3s linear;
}
.tb_records tr:hover td:first-child {
border-left:3px solid #4285F4;
}
.tb_records tr td:last-child {
border-right:3px solid #FFFFFF;
-webkit-transition:border-right 0.3s linear;
-o-transition:border-right 0.3s linear;
-moz-transition:border-right 0.3s linear;
transition:border-right 0.3s linear;
}
.tb_records tr:hover td:last-child {
border-right:3px solid #4285F4;
}
<table class="tb_records">
<tr>
<th>Firstname</th>
<th>Lastname</th>
<th>Email</th>
<th>Phone</th>
</tr>
<tr>
<td>Alan</td>
<td>Bowers</td>
<td>ban@gmail.com</td>
<td>1234567890</td>
</tr>
<tr>
<td>Ben</td>
<td>Oliver</td>
<td>ben@gmail.com</td>
<td>1234567890</td>
</tr>
<tr>
<td>Chris</td>
<td>Armes</td>
<td>chris@gmail.com</td>
<td>1234567890</td>
</tr>
<tr>
<td>Paul</td>
<td>Black</td>
<td>peb@yahoo.com</td>
<td>1234567890</td>
</tr>
<tr>
<td>Sagar</td>
<td>Soni</td>
<td>sag@yahoo.co.uk</td>
<td>1234567890</td>
</tr>
</table>