We have developed a full Monte Carlo simulation code to evaluate the electric signals produced by ionizing particles crossing a silicon strip detector (SSD). This simulation can be applied in the design stage of a SSD, to optimize the detector parameters. All the physical processes leading to the generation of electron-hole (e-h) pairs in silicon have been taken into account. Induced current signals on the readout strips are evaluated applying the Shockley-Ramo's theorem to the charge carriers propagating inside the detector volume. A simulation of the readout electronics has been also implemented. The Monte Carlo results have been compared with experimental data taken with a 400 μm thick SSD.