**The purpose of the paper.** Substantiation of structure (design), parameters and operation modes of the improved vibratory finishing machine. Analysis of dynamical processes which occur during “lap over lap” dressing. **Investigation methodology. **Mathematical model of motion of the mechanical system of vibratory finishing machine was developed on the basis of Lagrange differential equations of the second order. For the purpose of describing friction between the working surfaces of the laps, the Coulomb friction model was used. Stiffness parameters of all elastic elements were modeled in accordance with the Hooke’s law. Energy losses in elastic elements during their tension-compression were taken into account by corresponding coefficients of dissipation (damping). Simulation modelling of motion of the machine’s mechanical oscillatory system was carried out in MathCAD software by means of solving the derived differential equations of the system’s motion using the numerical methods of Runge-Kutta. **Obtained** **results****.** Structural and functional peculiarities of the improved vibratory finishing machine for lapping flat surfaces of cylindric and prismatic parts were considered. Design (calculation) diagram of its mechanical oscillatory system was substantiated and differential equations of motion of oscillating masses were derived. Simulation modelling of the laps’ motion during their dressing was carried out and the correspondence of the obtained results to the input modelling parameters (operation in near-resonance mode with the given oscillation amplitudes) was analyzed. **Scientific novelty.** For the first time we obtained following results: spatial design (calculation) diagram of mechanical oscillatory system of the improved vibratory finishing machine was proposed; mathematical model of plane-parallel motion of oscillating masses (with circular trajectories of oscillations) was developed; possibilities of performing the laps dressing using “lap over lap” method were substantiated by means of ensuring their circular oscillations. **Practical** **value****. **The results of the performed investigations can be used during designing new and improving existing structures of vibratory finishing machines for finishing treatment (lapping) of flat surfaces of cylindric and prismatic parts.

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