Cavities have been laser ablated in the ends of single-mode optical fibers and sealed by aluminized polycarbonate diaphragms to produce Fabry-Perot pressure sensors. Both conventional fibers and novel, multicore fibers were used, demonstrating the possibility of producing compact arrays of sensors and multiple sensors on an individual fiber 125 microm in diameter. This high spatial resolution can be combined with high temporal resolution by simultaneously interrogating the sensors by using separate laser sources at three wavelengths. Shock tube tests showed a sensor response time of 3 micros to a step increase in pressure.