In this paper we show two results on PRAM with constant fraction of memory faults. First we show how to preprocess (i.e. connect a constant fraction of processors into a binary tree) a faulty EREW PRAM with n/log n processors and O(n) memory cells in 0(log n) time. The preprocessing is a basic step of simulations from [7, 9, 17]. Our algorithm, together with the results from , gives a first fully work-optimal randomized simulations of EREW on EREW with faults with logarithmic overhead. In the second part of this paper, we consider the CRCW PRAM with memory faults. We show that (after 0(log n)-time preprocessing) any algorithm for 0(n)-processor PRAM can be simulated with optimal work in 0(log * n) time on CRCW with memory faults. The simulation improves the result of , All simulations assume static faults, i.e. that the errors are determined before the computation starts and that no new errors occur during the computation.