Differential cross sections for elastic scattering of positive pions on O16 at 40.0 and 49.7 MeV were measured at about 10°intervals for laboratory angles from 25°to 160°. Relative uncertainties between angles are 3%, with the overall normalization known to 7% for each angular distribution. The angular distributions are similar in shape, being dominated by a minimum at about 60°. The differential cross sections are presented along with the results of a partial wave analysis which gives good fits at both 40.0 and 49.7 MeV. The data are also fitted by a simple phenomenological first-order Kisslinger nonlocal optical model calculation. NUCLEAR REACTIONS O16(π+,π+)O16. E=40.0,49.7 MeV, θ=25-160°, measured σ(θ,E). Partial-wave and optical model analyses of σ(θ,E).