A detailed calculation is presented of the generation of large-scale streaming velocities by nonsuperconducting cosmic strings. A spherical infall model is used to calculate the peculiar velocity induced by an individual loop of cosmic string at rest in the comoving frame. The effects of many uncorrelated loops are combined using both a semianalytic method and Monte Carlo simulations. The calculations are modified to include loop correlations. The results show that cosmic strings and cold dark matter are in apparent conflict with observations, but cosmic strings and hot dark mattter offer a hope of explaining the reported large-scale streaming velocities. 37 references.