We study Majorana zero-mode properties in cylindrical cross-section semiconductor quantum wires based on the effective-mass theory and a discretized lattice model. Within this model the influence of disordered potentials in the quantum wire as well as amplitude and phase fluctuations of the superconducting order parameter are discussed. We find that for typical wire geometries, pairing potentials, and spin-orbit coupling strengths, coupling between quasi-one-dimensional subbands is weak, low-energy quasiparticles near the Fermi energy are nearly completely spin polarized, and the number of electrons in the active subbands of topological states is less than 10.