A method for digitally processing audio signals to emulate the effects of vacuum tube amplifiers and preamplifiers, musical instrument amplification systems, and distortion effects. By use of a parametrically-controlled non-linear transfer function, non-linear filters, feedback elements, and power-law function models, the dynamic behavior and distortion effects of tube amplification stages are simulated. This provides users with the capability to reproduce the desired sounds of vintage and modern tube amplifier systems and effects with the conveniences and control associated with digital signal processing systems and software.