Experiments carried out at the ISKRA-5 facility have demonstrated high (not worse than 3%) symmetry of the X-ray radiation flux inside a spherical case (hohlraum). This fact gave us an opportunity for investigating into compression of the targets with the initial nonspherical geometry. The asymmetry affects both the total neutron yield and the moment of neutrons generation. In this paper we present the simulation results of the asymmetric targets dynamics which were carried out by means of the 2D MIMOZA-ND code. This code allows to take into account effects of nonstationary, nonequilibrium, spectral transfer of X-ray radiation. Comparison between simulation results and experimental data was made. It was demonstrated that one could observe a satisfactory agreement between experimental data and the total neutron yield, as well as the time delay of the moment of neutrons generation.