During filtration of a fluid-solid mixture, a filter cake composed of solids is formed on the upstream side of the permeable interface—the filtrate or clean fluid passes through but not the solids. This paper describes a multi-dimensional calculation framework to carry out numerical simulations of growth and deformation of a filter cake. Two examples of cake growth and deformation phenomena of interest to the oil industry are the sticking of drill string within a wellbore and the sealing of wellbore sections by expandable packers. The calculation algorithm is based on the algebraic slip mixture model, involving the solution of a non-linear transport equation for solids concentration and the mass- and momentum-conservation equations of the mixture for the velocity and pressure field. The matrix stress and flow permeability are expressed as functions of solids concentration. The viscosity in the momentum equations is modeled using the Bingham approach and proportionality between yield stress and solids matrix pressure. Velocity and pressure fields are split into filtration and deformation components, thus permitting a stable calculation scheme. The simulated results match reasonably experimental observations.