It is advantageous to use the method of surface plastic deformation in order to get high-quality surfaces that meet increased requirements for strength and reliability. For efficient process of surface plastic deformation, it is required to define a set of conditions to provide minimum roughness of a machined surface. The paper addresses the problem of experimental search of optimal burnishing modes using the simplex design to minimize roughness of a machined surface. The significance of variable factor ranking was observed for this technique. A specific set of tests resulted in decrease in the initial surface roughness almost by 15 times in the specimens made of aluminum alloy after burnishing with the steel indenter. It was established that the surface quality was significantly affected by a new factor – angle of indenter contact with the machined surface, which had a damping effect on the machine-fixture-tool-workpiece system. The experiments showed that polished indenter balls significantly lowered the roughness grade of the machined surface under the same conditions.