The stability of a field-reversed mirror plasma configuration is studied with an energyprinciple derived from the Vlasov equation. Because of finite orbit effects, the stability properties of a fieldreversedmirror are different from the stability properties of similar magnetohydrodynamic equilibria. TheVlasov energy principle developed here is applied to a computer simulation of an axisymmetric field-reversedmirror state. Possible instabilities with ℓ = 1, 2 are found at low growth rate. A simple physical model for thisinstability is outlined.