Regulation of actin polymerization is essential for cell functioning. Here, we predict a novel phenomenon—the force-driven polymerization of actin filaments mediated by proteins of the formin family. Formins localize to the barbed ends of actin filaments, but, in contrast to the standard capping proteins, allow for actin polymerization in the barbed direction. First, we show that the mechanism of such “leaky capping” can be understood in terms of the elasticity of the formin molecules. Second, we demonstrate that if a pulling force acts on the filament end via the leaky cap, the elastic stresses can drive actin polymerization. We estimate that a moderate pulling force of ∼3.4 pN is sufficient to reduce the critical actin concentration required for barbed end polymerization by an order of magnitude. Furthermore, the pulling force increases the polymerization rate. The suggested mechanism of force-driven polymerization could be a key element in a variety of cellular mechanosensing devices.