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Reflector antennas with mesh surfaces are used extensively in many satellite and ground antenna systems. A strip-aperture modeling of commonly used mesh surfaces is presented which provides considerable versatility in characterizing the mesh cells. The mesh transmission coefficients are constructed using a Floquet-modal expansion in conjuction with two dominant aperture modes. To account for the mesh local coordinates, the Eulerian angle transformation is invoked to obtain the total induced current on the curved reflector surface. General formulas are presented to show how the solid surface induced current is modified due to the transmission through the mesh. The effects of a variety of mesh configurations on both the co-polar and cross-polar patterns of reflector antennas are studied by numerically evaluating the vector diffraction integral using the Jacobi-Bessel expansion. For some special cases, a comparison is made with the results of the commonly used wire-grid formulation. Many of the numerical data are tailored to the dimensions of a conceptually designed mesh deployable offset reflector of the land mobile satellite system (LMSS).