We consider the heating and acceleration of electrons trapped on magnetic field lines between approaching magnetic mirrors. Such a collapsing magnetic trap and consequent electron energization can occur whenever a curved (or straight) flux tube drifts into a relatively straight (or curved) perpendicular shock. Our relativistic, three-dimensional, collisionless test particle simulations show that an initial thermal electron distribution is bulk heated while a few individual electrons are accelerated to many times their original energy before they escape the trap. Upstream field-aligned beams and downstream pancake distributions perpendicular to the field are predicted. In the appropriate limit the simulation results agree well with a nonrelativistic analytic model of the distribution of escaping electrons which is based on the first adiabatic invariant and energy conservation between collisions with the mirrors. Space science and astrophysical applications are discussed. ¿ American Geophysical Union 1990