The term roughness is used to describe a specific sound sensation which may occur when listening to stimuli with more than one spectral component within the same critical band. It is believed that the spectral components interact inside the cochlea, which leads to fluctuations in the neural signal and, in turn, to a sensation of roughness. This study presents a roughness model composed of two successive stages: peripheral and central. The peripheral stage models the function of the peripheral ear. The central stage predicts roughness from the temporal envelope of the signal processed by the peripheral stage. The roughness model was shown to account for the perceived roughness of various types of acoustic stimuli, including the stimuli with temporal envelopes that are not sinusoidal. It thus accounted for effects of the phase and the shape of the temporal envelope on roughness. The model performance was poor for unmodulated bandpass noise stimuli.