Homogeneous rapid distortion theory is used to study the response of shear flows and axisymmetric turbulence to rapid one-dimensional compression. In the shear flow problem, both normal and oblique compressions are considered. The response of these anisotropic flows to compression is found to be quite different from that of isotropic turbulence. Upon normal compression, the amplification of the streamwise component of kinetic energy and the total kinetic energy in shear flows is higher than that in isotropic turbulence. Also, normal compression decreases the magnitude of the Reynolds shear stress by amplifying the pressure-strain correlation in the shear stress equation. Obliquity of compression (defined as the angle between the directions of shear and compression) is seen to significantly affect the evolution of the Reynolds stresses. For a range of oblique angles from -60° to 60°, the amplification of streamwise kinetic energy and total kinetic energy decrease with increasing magnitude of the oblique angle. Also, the tendency of the shear stress to decrease in magnitude is diminished upon increasing the oblique angle; for large oblique angles the shear stress amplifies. Upon compression along the axis of axisymmetry, the amplification of the streamwise component of kinetic energy is higher for contracted turbulence than for isotropic turbulence, while the amplification of the total kinetic energy is lower. The above results are interpreted in a more general framework. It is shown that the amplification of the streamwise component of kinetic energy is determined by the initial E 11(κ1) (x1 is the direction of compression). Flows with u1 at lower κ1 have a lower effect of pressure during compression and hence, higher amplification of u 12. The amplification of the total kinetic energy is determined by the initial fraction of energy along the direction of compression (u12/q2) and the initial E11(κ 1). Flows with higher initial u12/q2 and with u1 at lower κ1 have a larger amplification of q2.