To allow your form to upload files, it should have the enctype="multipart/form-data"
attribute.
You can do it like so:
@using (Html.BeginForm("Action", "Controller", FormMethod.Post, new{ enctype="multipart/form-data" }))
{
@Html.ValidationSummary(true)
@Html.TextBoxFor(a => a.Attachment, new { @type = "file" })
}