Weak gravitational lensing studies of galaxy clusters often assume a spherical cluster model to simplify the analysis, but some recent studies have suggested this simplifying assumption may result in large biases in estimated cluster masses and concentration values, since clusters are expected to exhibit triaxiality. Several such analyses have, however, quoted expressions for the spatial derivatives of the lensing potential in triaxial models, which are open to misinterpretation. In this paper, we give a clear description of weak lensing by triaxial NFW galaxy clusters and also present an efficient and robust method to model these clusters and obtain parameter estimates. By considering four highly triaxial NFW galaxy clusters, we re-examine the impact of simplifying spherical assumptions and found that while the concentration estimates are largely unbiased except in one of our traixial NFW simulated clusters, for which the concentration is only slightly biased, the masses are significantly biased, by up to 40%, for all the clusters we analysed. Moreover, we find that such assumptions can lead to the erroneous conclusion that some substructure is present in the galaxy clusters or, even worse, that multiple galaxy clusters are present in the field. Our cluster fitting method also allows one to answer the question of whether a given cluster exhibits triaxiality or a simple spherical model is good enough.
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