ABSTRACT. We examine the effects of charge transfer inefficiency (CTI) during CCD readout on the demanding galaxy shape measurements required by studies of weak gravitational lensing. We simulate a CCD readout with CTI such as that caused by charged particle radiation damage in space-based detectors. We verify our simulations on real data from fully depleted p-channel CCDs that have been deliberately irradiated in a laboratory. We show that only charge traps with time constants of the same order as the time between row transfers during readout affect galaxy shape measurements. We simulate deep astronomical images and the process of CCD readout, characterizing the effects of CTI on various galaxy populations. Our code and methods are general and can be applied to any CCDs, once the density and characteristic release times of their charge trap species are known. We baseline our study around p-channel CCDs that have been shown to have charge transfer efficiency up to an order of magnitude better than several models of n-channel CCDs designed for space applications. We predict that for galaxies furthest from the readout registers, bias in the measurement of galaxy shapes, Δe, will increase at a rate of ð2:65 AE 0:02Þ × 10 À4 yr À1 at L2 for accumulated radiation exposure averaged over the solar cycle. If uncorrected, this will consume the entire shape measurement error budget of a dark energy mission surveying the entire extragalactic sky within about 4 yr of accumulated radiation damage. However, software mitigation techniques demonstrated elsewhere can reduce this by a factor of ∼10, bringing the effect well below mission requirements. This conclusion is valid only for the p-channel CCDs we have modeled; CCDs with higher CTI will fare worse and may not meet the requirements of future dark energy missions. We also discuss additional ways in which hardware could be designed to further minimize the impact of CTI.