By replacing the traditional single magnetic free layer in magnetic random access memory (MRAM) with a free layer composed of two antiferromagnetically coupled layers which switch by spin flop switching, the half select and activation energy problems that have hindered progress in MRAM to date can be essentially eliminated. By analytically and numerically solving a single domain model, the theory of spin flop switching for MRAM is developed here, including a discussion of the various types of easy axis hysteresis loops, the critical switching curve as a function of word and bit line fields, the role of thickness asymmetry, and the dependence of activation energy on applied field. The theory is developed for arbitrary thickness, length, width, magnetization, intrinsic anisotropy, and exchange coupling. Exact analytic formulas are given for the relevant switching fields and the activation energy. In particular, it is shown that the field required to switch the bit under half select can be many times larger than the field required for full select, and furthermore that the activation energy initially increases under application of a half select field.