The slow light effect in semiconductor optical amplifiers has many potential applications in microwave photonics such as phase shifting and filtering. Models are needed to predict the slow light effect in SOAs and its dependence on the bias current, wavelength, and power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a detailed carrier density rate equation and travelling-wave equations for the amplitude modulated signal and amplified spontaneous emission. The slow light parameters of interest include the beat signal phase shift and amplitude response. The model predictions show good agreement with experimental trends reported in the literature.