The scientific article presents the results of research to identify the regularities arising from the abrasive finishing of the surfaces of parts made of aluminium alloy grade (AMts) in a magnetic field. As a result of conducted experiments the relations between variable factors of abrasive finishing in a magnetic field and quality indicators of surfaces of parts from aluminium alloy of mark AMts which have been expressed by means of physical and statistical model of graphic dependences of functions defined as Ra = f(t, n) and Ra = f(B, S). It has been established that abrasive finishing in a magnetic field allows for an insignificant amount of time t = 4...12 min to reduce surface roughness from initial Ra = 1.3...1.9 μm to Ra = 0.23...0.85 μm (depending on processing conditions). In addition, the optimization problem of determining the optimal conditions of abrasive finishing in a magnetic field, providing the achievement of the minimum value of roughness Ramin = 0.23 μm of the surfaces of parts made of aluminium alloy grade AMts was solved.