Using fits to the available data on the pion and deuteron electromagnetic form factors and the Chou-Yang model, the computed values of differential cross-sections for high-energy pion-deuteron elastic scattering agree reasonably well with the available experimental data. Whereas only a shoulder is expected to appear up to energies of several hundreds of GeV, a dip and a secondary maximum are predicted to be conspicuous only forP_lab≫400 GeV/C. The position of the dip starts at a much lower value, |t_d| ≅ 0.5–0.6 GeV², as compared to the corresponding position in thepp scattering. The positions of the first dip are plotted against total cross-section which can be verified by future high-energy experiments. Limitations of the model predictions for ultrahigh energies are pointed out.