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The surface stresses along the contour of a crack-tip craze in a glassy thermoplastic can be computed from measured craze displacements by applying finite element methods. It is shown that calculated crack-tip craze surface stress distributions are highly dependent on the accuracy of the evaluation of the elastic modulus of the bulk polymer. Methods of estimating the modulus are considered. A method based on fitting the Dugdale model to the measured craze profile gives rate- and time-dependent moduli which are consistent with measured moduli at strain levels comparable with those in the compact tension specimen near the interface with the craze. The major part of the sample is at a much lower strain level and a new method, based on interference optical measurements and finite element computations of crack displacements, is developed to estimate the appropriate modulus. Craze surface stresses are computed for two cases in which the estimated modulus for the two parts of the sample significantly differ. In a creep test, the modulus near the craze is lower than that in the remainder of the specimen and it is seen that any stress concentration at the crack tip is suppressed. This explains why the crack remains stationary while the craze continues to grow. In the case of crack propagation, the modulus in the region around the craze has the higher value and the stress at the crack tip increases. The crack therefore continues to propagate.