The anelastic approximation (AA) filters out fast moving waves, chiefly sound waves and fast magneto-acoustic waves. This filtering allows numerical schemes to take much larger time-steps. To make the AA we assume the Mach number of the flow must be small. A further assumption that the basic state is isentropic is used in some anelastic equations. This extra assumption allows the thermodynamic variables to be written in terms only of the entropy which creates a large computational saving. My work is concerned with the uses of the AA and a isentropic AA. Modern anelastic codes have been used in the sun for global simulations from the tachocline to the corona. This is not valid in regions of the sun that are strongly sub-adiabatic. I will discuss where the AA and the isentropic AA break down.