We present a systematic pressure study of poly- and single crystalline SrFe2As2 by electrical resistivity and X-ray diffraction measurements. SrFe2As2 exhibits a structural phase transition from a tetragonal to an orthorhombic phase at T0=205 K. The structural phase transition is intimately linked to a spin-density-wave transition taking place at the same temperature. Our pressure experiments show that T0 shifts to lower temperatures with increasing pressure. We can estimate a critical pressure of 4 to 5 GPa for the suppression of T0 to zero temperature. At pressures above 2.5 GPa the resistivity decreases significantly below Tx=40 K hinting at the emergence of superconductivity but no zero-resistance state is observed up to 3 GPa.