Exclusive semileptonic decays of bottom and charm baryons are considered within a relativistic three-quark model with a Gaussian shape for the baryon-three-quark vertex and standard quark propagators. We calculate the baryonic Isgur-Wise functions, decay rates and asymmetry parameters. PACS: 12.39.Ki, 13.30.Ce, 14.20.Lq, 14.20.Mr