Antiproton-proton elastic scattering was measured at c.m.s. energies s**(1/2) = 546 and 1800 GeV in the range of four-momentum transfer squared 0.025 < -t < 0.29 GeV2. The data are well described by the exponential form ebt with a slope b = 15.28 +/- 0.58 (16.98 +/- 0.25) GeV-2 at s**(1/2) = 546 (1800) GeV. The elastic scattering cross sections are, respectively, sigma_el = 12.87 +/- 0.30 and 19.70 +/- 0.85 mb.