The telephone sound effect is widely used in music, television and the film industry. This paper presents a digital model of the carbon microphone nonlinearity which can be used to produce a vintage telephone sound effect. The model is constructed based on measurements taken from a real carbon microphone. The proposed model is a modified version of the sandwich model previously used for nonlinear telephone handset modeling. Each distortion component can be modeled individually based on the desired features. The computational efficiency can be increased by lumping the spectral processing of the individual distortion components together. The model incorporates a filtered noise source to model the self-induced noise generated by the carbon microphones. The model has also an input level depended noise generator for additional sound quality degradation. The proposed model can be used in various ways in the digital modeling of the vintage telephone sound.