The extent and dynamics of actin polymerization in solution are calculated as functions of the filament severing rate, using a simple model of in vitro polymerization. The model is solved by both analytic theory and stochastic-growth simulation. The results show that severing essentially always enhances actin polymerization by freeing up barbed ends, if barbed-end cappers are present. Severing has much weaker effects if only pointed-end cappers are present. In the early stages of polymerization, the polymerized-actin concentration grows exponentially as a function of time. The exponential growth rate is given in terms of the severing rate, and the latter is given in terms of the maximum slope in a polymerization time course. Severing and branching are found to act synergistically.