We report ensemble Monte Carlo transport simulation results for single-wall semiconducting zigzag carbon nanotubes. The effects of electron scattering by radial breathing mode phonons are investigated. The basis for the Monte Carlo simulations is provided by electronic structure calculations in the framework of the tight-binding model. Scattering mechanisms considered are due to electron-phonon interactions involving longitudinal acoustic, longitudinal optical, and radial breathing mode phonons. The steady-state velocity is lower for low and moderate electric fields when radial breathing mode phonons are taken into account. Electron scattering by radial breathing mode phonons does not appear to affect strongly the steady-state electron transport within a carbon nanotube at high electric fields. Oscillations in the transient velocity show increased damping.