The theory of kinetic instabilities in a plasma when the instabilities are driven by wave‐particle resonance is addressed. Recent progress on the linear theory of resonant oblique wave growth in plasmas is extended to plasmas modeled by three standard forms of distribution, a bi‐Maxwellian, a bi‐Lorenzian, and a loss cone, each incorporating a field‐aligned beam. The wave growth rates are shown to be functions of dimensionless integrals that can be expressed in terms of Bessel functions of argument equal to a normalized wave‐normal variable. A marginal stability criterion is obtained, and accordingly we identify a threshold beam velocity for unstable growth of the waves. The simple analytical results derived can be readily applied to a wide variety of problems on oblique wave growth in space plasmas that hitherto were amenable only to extensive computer calculations.