The cone-beam tomographic projection and the deformation of a discrete volume are problems that have generally been studied separately. They are combined in some applications such as motion compensated algebraic reconstruction. In this paper, we propose two methods to compute the cone-beam projections of a volume deformed with a known motion. The first method is based on an inverse mapping between the reference 3D volume and the 2D cone-beam projection and the second method on a forward mapping. Both methods were evaluated on a dynamic digital phantom and confronted to another method. The quality of the cone-beam projections was increased by 70% with both methods compared to the projection obtained without including the motion model. The proposed methods yield accurate linear equations, the first step before tomographic reconstruction of the deformable volume with algebraic methods.