A classical Boltzmann model of cyclotron resonance with an energy-independent collision time is developed. An approximate solution of the Boltzmann equation is obtained by expanding the perturbed distribution function Φ(p, Θ, φ), in a Fourier series in φ, where the spherical coordinates are defined with the polar axis along the magnetic field direction. The solution yields a fundamental cyclotron resonance absorption line, which shows line shape anisotropy, as well as a shift in resonance peak with magnetic field direction. The theory also indicates resonance absorption at harmonics of the fundamental cyclotron resonance frequency, due to the warping of the constant-energy surfaces. The results are applied to a calculation of line shapes and harmonic intensities for heavy holes in silicon and germanium.