Until recently, simple and reliable high repetition-rate laser sources with nanosecond pulses much shorter than from conventional A-O Q-switch lasers were not available. However over the past 2 years we have developed such lasers based on proprietary fast E-O switching technology, which allows designs delivering ~1ns pulses and subnanosecond jitter for good synchronisation. The technology provides pulses with multi-kW peak power and repetition-rates to >100kHz.Most recently, the performance of these short pulse lasers has been developed further by implementing oscillator/amplifier (master oscillator and power amplifier, MOPA) technology which increases the output to >1W average power. Here we report on a simple model that has been used to predict the performance of the CW pumped Nd:YVO 4 amplifier used in the MOPA laser. The model is based on the well-known expressions for the saturated gain applying to laser pulses, but more usually applied to pulse-excited amplifiers. The model is shown to allow a good interpretation of the amplifier behaviour for kHz pulses and to be a useful tool for predicting the performance of the MOPA laser.