Numerical simulations of Rayleigh--Taylor and Richtmyer--Meshkov instability using MAH-3 code Results of the 2D and 3D numerical modeling of the Rayleigh--Taylor and the Richtmyer--Meshkov instabilities are presented. The modeling is performed by using the MAH-3 code enabling to solve nonsteady-state 3D gas-dynamic problems. Brief description of the numerical model is given. For the Rayleigh--Taylor instability, the evolution of single-mode interface perturbations is studied both at the linear and nonlinear stages. The case of the Richtmyer--Meshkov instability is considered to investigate the evolution of single-mode perturbations into the turbulent stage. Single-mode perturbation growth rates are compared for the cases of the 2D and 3D modeling. To represent the growth of stochastic perturbations under the Rayleigh--Taylor instability in the calculations, conditions of diagnosing the stage of self-similar turbulent mixing were proposed.