Adsorption of p-H2 films on Alkali metals substrates at low temperature is studied theoretically by means of Path Integral Monte Carlo simulations. Realistic potentials are utilized to model the interaction between two p-H2 molecules, as well as between a p-H2 molecule and the substrate, assumed smooth. Results show that adsorption of p-H2 on a Lithium substrate, the most attractive among the Alkali, occurs through completion of successive solid adlayers. Each layer has a twodimensional density θe ≈ 0.070Å −2 . A solid p-H2 monolayer displays a higher degree of confinement, in the direction perpendicular to the substrate, than a monolayer Helium film, and has a melting temperature of about 6.5 K. The other Alkali substrates are not attractive enough to be wetted by H2 at low temperature. No evidence of a possible superfluid phase of p-H2 is seen in these systems.