The possibility that fast electrons can escape in a direction close to the trajectory of a reflected ultrashort laser pulse at extremely high laser radiation fluxes is examined analytically and numerically. Analytic estimates are made of the feasibility of forming electron bursts in the plasma and of their subsequent motion. The self-consistent, collisionless motion of a plasma acted on by specified incident and reflected ultrashort laser pulses is modeled in two dimensions by the particle-in-cell method. It is shown that a substantial number of electrons located in the subcritical region are gathered into bunches by the resultant forces and escape to the vacuum in a direction different from the normal to the target surface within a narrow range of solid angles. This demonstrates the feasibility of laser acceleration of an electron burst during reflection of an ultrashort laser pulse from a solid target.