We present a simple method for accessing the elastic properties of microscopic deformable particles. This method is based on measuring the pressure-induced deformation of soft particles as they are forced through a tapered glass microcapillary. It allows us to determine both the compressive and the shear modulus of a deformable object in one single experiment. Measurements on a model system of poly-acrylamide microgel particles exhibit excellent agreement with measurements on bulk gels of identical composition. Our approach is applicable over a wide range of mechanical properties and should thus be a valuable tool for the characterization of a variety of soft and biological materials