Low-temperature adsorption of ⁴He films on Alkali metal substrates is investigated theoretically by means of ground-state quantum Monte Carlo simulations. The most accurate potentials currently available are utilized to model the interaction of ⁴He atoms with the substrate. Continuous growth of film thickness as a function of chemical potential is observed on Li, Na, and K substrates. A superfluid monolayer forms on a Li substrate; on Na and K, thermodynamically stable films are a few layers thick. The uncertainties of the calculation and in the potentials, preclude a definitive conclusion on the existence of a stable ⁴He film on Rb. A comparison of the results of this calculation with those obtained using the Orsay-Trento density functional shows broad quantitative agreement.