Detailed numerical models of X-ray bursts resulting from thermonuclear flashes near the surface of an accreting neutron star have been constructed. The models assume a nonrotating nonmagnetized spherically accreting neutron star of 1.4 solar masses, radius 6.6 km, core temperature in the range from 250 million to 570 million K, and accretion rate in the range (0.3-3) x 10 to the 17th power g/s. Under many conditions the helium-burning shell undergoes thermonuclear flashes that result in the emission of X-ray bursts, the gross properties of which are remarkably similar to those of most observed X-ray burst sources. Neutron stars with moderately low core temperatures, low accretion rates, and weak magnetic fields are most likely to produce X-ray bursts.