Differential cross sections for elastic scattering of 40 MeV positive pions from 12C, 16O, 40Ca, 90Zr, and 208Pb were measured at 18 angles in the angular range 25°-160°. Relative uncertainties of 2.5% to 7% and overall normalization uncertainties of 4% to 7% were obtained. An optical potential fit of the data indicates that while the magnitudes of the strength parameters, except for Reb1, are different from values obtained from free πN scattering amplitudes, the variation of these magnitudes with target mass is roughly as predicted by the impulse approximation. Coulomb effects, especially in the cases of 90Zr and 208Pb, are extremely important, but impossible to unambiguously separate from the strong interaction in the optical model. NUCLEAR REACTIONS Elastic scattering of 40 MeV π+ from 12C, 16O, 40Ca, 90Zr, 208Pb. Angular distributions: 25°<θL<160°. Optical model and partialwave analysis of cross-section data.