A pressure relief valve comprises a valve body which includes an inlet bore that is connectable to a flow line, an outlet bore that is connectable to a vent line and a valve bore that extends to between the inlet and outlet bores. A valve member is axially movable in the valve bore between a closed position in which fluid in the flow line is prevented from flowing between the inlet and outlet bores and an open position in which the fluid in the flow line is permitted to flow between the inlet and outlet bores. A fluid chamber is located in the valve bore adjacent the valve member, a source of hydraulic fluid is connected to the fluid chamber, and a solenoid operated pilot valve is connected between the fluid chamber and the source of hydraulic fluid. During operation of the pressure relief valve, the pilot valve is opened to fill the fluid chamber with hydraulic fluid, then is closed to trap the hydraulic fluid in the fluid chamber and thereby maintain the valve member in its closed position against pressure in the flow line, and then, when the pressure in the flow line reaches a predetermined level, is opened to release the hydraulic fluid from the fluid chamber and thereby allow the valve member to move from its closed position to its open position.