This paper reports on a technique for fabricating intrinsic fibre Fabry-Perot cavities in fused silica optical fibres. An F-2-excimer laser was used to micromachine parallel walled cavities through the diameter of optical fibres. A custom-designed beam delivery and target alignment system was used to enable the production of high aspect-ratio cavities in fibres. The optical response of the micro-cavities ablated in SMF 28 and SM 800 fibres at suitable energy densities showed Fabry-Perot fringes produced as a result of interference of Fresnel reflections at the cavity wall surfaces. The intrinsic fibre Fabry-Perot cavities were characterized using optical and scanning electron microscopy. Preliminary tests have shown that these intrinsic cavities can be used as strain sensors.