We present here a mechanics model for the force generation by actin polymerization. The possible adhesions between the actin filaments and the load surface, as well as the nucleation and capping of filament tips, are included in this model on top of the well-known elastic Brownian ratchet formulation. A closed form solution is provided from which the force-velocity relationship, summarizing the mechanics of polymerization, can be drawn. Model predictions on the velocity of moving beads driven by actin polymerization are consistent with experiment observations. This model also seems capable of explaining the enhanced actin-based motility of Listeria monocytogenes and beads by the presence of Vasodilator-stimulated phosphoprotein, as observed in recent experiments.