Electron beam-induced deposition (EBID) provides a simple way to fabricate submicron- or nanometerscale structures from various elements in a scanning electron microscope (SEM). The growth rate and shape of the deposits are influenced by many factors. We have studied the growth rate and morphology of EBID-deposited nanostructures as a function of the tungsten hexafluoride (WF6) and tetraethylorthosilicate (TEOS) precursor gas pressure and growth time, and we have used Monte Carlo simulations to model the growth of tungsten and silicon oxide to elucidate the mechanisms involved in the EBID growth. The lateral radius of the deposit decreases with increasing pressure because of the enhanced vertical growth rate which limits competing lateral broadening produced by secondary and forward-scattered electrons. The morphology difference between the conical SiOx and the cylindrical W nanopillars is related to the difference in interaction volume between the two materials. A key parameter is the residence time of the precursor gas molecules. This is an exponential function of the surface temperature; it changes during nanopillar growth and is a function of the nanopillar material and the beam conditions.