A possible mechanism for uniaxial anisotropy in ferromagnetic films is the magnetoelastic energyW&lgr;which results from the constraint imposed on the film by the substrate. Below some temperatureT′ at which the mobility of the film atoms on the substrate is sufficiently low, the constraint prevents the film from deforming in magnetostriction. An increase in the magnetoelastic energy, therefore, occurs when the film is magnetized in a direction other than that in which the film was deposited.This paper examines this constraint energy in detail and shows that earlier calculations which have been based on the average polycrystalline magnetostriction are not correct in principle, since the correct calculation requires averaging the magnetoelastic energy over a polycrystalline aggregate. For the maximum value ofW&lgr;at room temperature the correct calculation gives 4.2, 1.8, and 42 (103erg cm−3) in nickel, iron, and cobalt, respectively. The value for iron is an order of magnitude larger than that given by earlier calculations. These values are found to be consistent with the experimental results of several groups of workers for films of nickel, iron, and cobalt deposited on amorphous substrates in vacua of less than about 10−5Torr and for electrodeposited films of nickel and cobalt. The particular case of the temperature dependence ofW&lgr;in nickel films is found to be in agreement with the reported experimental behavior when annealing of the constraint is allowed for. The annealing kinetics are discussed qualitatively in the light of observations by Benjamin and Weaver on film‐substrate adhesion. This discussion predicts, in agreement with experiment, the possibility of room‐temperature magnetic annealing in films deposited on unheated glass substrates in good vacua.Evidence is also presented for the presence of constraint energy in evaporated films of the nickel‐iron alloys, particularly near the 50% Ni composition. The calculations for the maximum room‐temperature values ofW&lgr;give a maximum of 3×103erg cm−3at 50% Ni and a minimum of about 20 erg cm−3at 82% Ni.