The numerical technique for simulation of viscous non-linear interactions between a solitary wave and a non-regular bottom was developed. It couples the boundary integral method used to determine the free surface deformations and the vortex scheme for integrating the fluid dynamic equations. To verify the model, a series of test calculations was carried out, where the obtained results were compared with our own experimental data and results known from similar studies by other authors. A good coincidence of the free surface elevation, as well as the velocity fields during the passage of a solitary wave over a thin submerged plate, was obtained. Systematic calculations of the interaction of a solitary wave with a submerged step in a wide range of wave amplitudes and step heights were performed. It is shown that when a wave emerges from deep water into the shallows, its evolution is determined by energy losses due to reflection, dispersion effects, and the generation of a vortex field. The dynamics of the wave on the submerged step depends on the coefficient of interaction, which is the ratio of the wave amplitude to the water depth above the step. Four types of wave behavior are possible above the step. Those are the weak interaction, when the wave gently splits into transmitted and reflected solitons; fission with development of two solitons behind the irregularity; fission with the generation of a dispersion chain of waves in the shallow water; and the collapse of a wave. The obtained critical value of the coefficient of interaction, at which the solitary wave is always breaking, is about 0.8, which is in congruence with the experimental data. Studies of patterns of vorticity generated by a solitary wave at the edge of a submerged step revealed two oppositely directed vortices with a horizontal axis, the scale of which is proportional to the water depth in a shallow channel. Their dynamics causes intensive exchange processes between deep water and shallows, as well as water flows from the bottom to the top and water mixing. The obtained data make it possible to predict in advance the development of processes and dangers caused by long nonlinear waves reaching the shelf.