  A virtual knot that has a homologically trivial representative $\mathscr{K}$
in a thickened surface $\Sigma \times [0,1]$ is said to be an almost classical
(AC) knot. $\mathscr{K}$ then bounds a Seifert surface $F\subset \Sigma \times
[0,1]$. Seifert surfaces of AC knots are useful for computing concordance
invariants and slice obstructions. However, Seifert surfaces in $\Sigma \times
[0,1]$ are difficult to construct. Here we introduce virtual Seifert surfaces
of AC knots. These are planar figures representing $F \subset \Sigma \times
[0,1]$. An algorithm for constructing a virtual Seifert surface from a Gauss
diagram is given. This is applied to computing signatures and Alexander
polynomials of AC knots. A canonical genus of AC knots is also studied. It is
shown to be distinct from the virtual canonical genus of
Stoimenow-Tchernov-Vdovina.
