(Abridged) We study predictions for galaxy cluster observables that can test the statistics of dark matter halo shapes expected in a flat LCDM universe. We present a simple analytical model for the prediction of cluster-scale X-ray observations, approximating clusters as isothermal systems in hydrostatic equilibrium, and dark matter haloes as ellipsoids with uniform axial ratios. We test the model against high-resolution, hydrodynamic cluster simulations to gauge its reliability. We find that this simple prescription does a good job of predicting the distribution of cluster X-ray ellipticities compared to the simulations as long as one focuses on cluster regions that are less sensitive to recent mergers. Based on this simple model, the distribution of cluster-size halo shapes expected in the concordance LCDM cosmology implies an X-ray ellipticity distribution with a mean of 0.32 +- 0.01 and a scatter of 0.14 +- 0.01 for the mass range (1-4)x10^{14} Msun/h. We find it important to include the mass dependence of halo shape to make comparisons to observational samples that contain many, very massive clusters. We analyse the systematics of four observational samples of cluster ellipticities and find that our results are statistically compatible with observations. In particular, we find remarkably good agreement between two recent ROSAT samples and LCDM predictions that DO NOT include gas cooling. We also test how well our analytical model can predict Sunyaev-Zeldovich decrement maps and find that it is less successful although still useful; the model does not perform as well as a function of flux level in this case because of the changing triaxiality of dark matter haloes as a function of radial distance. Both this effect and the changing alignment of isodensity shells of dark matter haloes leave an imprint on cluster gas...
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