The FH2 domains of formin family proteins act as processive cappers of actin filaments. Previously suggested stair-stepping mechanisms of processive capping imply that a formin cap rotates persistently in one direction with respect to the filament. This challenges the formin-mediated mechanism of intracellular cable formation. We suggest a novel scenario of processive capping that is driven by developing and relaxing torsion elastic stresses. Based on the recently discovered crystal structure of an FH2-actin complex, we propose a second mode of processive capping-the screw mode. Within the screw mode, the formin dimer rotates with respect to the actin filament in the direction opposite to that generated by the stair-stepping mode so that a combination of the two modes prevents persistent torsion strain accumulation. We determine an optimal regime of processive capping, whose essence is a periodic switch between the stair-stepping and screw modes. In this regime, elastic energy does not exceed feasible values, and supercoiling of actin filaments is prevented.