Flame-cutting of a large plate is simulated. Neglecting the heat flow in the cutting direction makes it possible to use a two-dimensional finite element method. A cross-section transverse to the cutting direction is modelled. Three different assumptions regarding the normal strain in the cutting direction are compared. They are called plane strain, generalized plane strain and plane deformation. They all give residual stresses that agree well with measurements. The plane deformation assumptions improve this agreement to achieve a low computational cost.