We present high-energy x-ray diffraction data under applied pressures up to p = 29 GPa, neutron diffraction measurements up to p = 1.1 GPa, and electrical resistance measurements up to p = 5.9 GPa, on SrCo2As2. Our x-ray diffraction data demonstrate that there is a first-order transition between the tetragonal (T) and collapsed-tetragonal (cT) phases, with an onset above approximately 6 GPa at T = 7 K. The pressure for the onset of the cT phase and the range of coexistence between the T and cT phases appears to be nearly temperature independent. The compressibility along the a-axis is the same for the T and cT phases whereas, along the c-axis, the cT phase is significantly stiffer, which may be due to the formation of an As-As bond in the cT phase. Our resistivity measurements found no evidence of superconductivity in SrCo2As2 for p <= 5.9 GPa and T >= 1.8 K. The resistivity data also show signatures consistent with a pressure-induced phase transition for p >= 5.5 GPa. Single-crystal neutron diffraction measurements performed up to 1.1 GPa in the T phase found no evidence of stripe-type or A-type antiferromagnetic ordering down to 10 K. Spin-polarized total-energy calculations demonstrate that the cT phase is the stable phase at high pressure with a c/a ratio of 2.54. Furthermore, these calculations indicate that the cT phase of SrCo2As2 should manifest either A-type antiferromagnetic or ferromagnetic order.