An exceptionally high electrostrictive response was observed in electron irradiated polyvinylidene fluoride-trifluoroethylene (P(VDF-TrFE)) copolymer. Moreover, the transverse strain of the material can be tuned over a large range by different sample treatment conditions. For example, in uniaxially stretched films, the strain can be comparable or even larger than the longitudinal strain, while in unstretched films, the transverse strain is quite small. The polarization and dielectric results also show that the material exhibits typical ferroelectric relaxor behavior with a high dielectric constant and low dielectric loss at room temperature. The results suggest that the electron irradiation breaks up the coherent polarization domain in normal ferroelectric P(VDF-TrFE) copolymer into nano-polar regions which transforms the material into a ferroelectric relaxor with an ultrahigh electrostrictive response.