The linear theory of Alfve´n ion‐cyclotron instability is extended by a rigorous treatment of plasma nonuniformity along the equilibrium magnetic field. A standard phase‐integral dispersion relation provides stability boundaries. Two ion distribution functions allow modeling of plasmas formed in various ways, including neutral‐beam injection both perpendicular and oblique to magnetic field lines. Stability results are quantitatively consistent with past and present experiments. The results further indicate that two important features of stable mirror cells in future experiments are large mirror ratios and pitch‐angle distributions that are broad or are peaked far from perpendicular to the magnetic field.