The problems of filtration of suspensions in porous media, which are an integral part of underground hydromechanics, are solved when designing foundations and underground structures. As a rule, suspended particles of a suspension are heterogeneous and differ in shape and size. A model of filtration of a multiparticle suspension in a porous medium is considered. During filtration, the sedimentation rates of particles depend on their sizes and are proportional to the corresponding filtration coefficients, which are a priori unknown. In laboratory experiments, it is possible to determine the total concentration of suspended particles of a suspension at the porous sample inlet and outlet. The filtration coefficients are expressed from measured suspended concentrations. The article proposes a method for solving the inverse problem based on an explicit exact solution of the direct filtration problem at the concentration front. The inverse problem is reduced to a system of nonlinear algebraic equations. For a bidisperse suspension, an exact solution is found; for a multiparticle suspension, the inverse problem is solved numerically. The conditions necessary for the solution existence are derived.