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Based on the linearized Eilenberger equations, the upper critical field$(H_{c2})$ of mixed d- and s-wave superconductors has been microscopicallystudied with an emphasis on the competing effects of mass anisotropy and spinZeeman coupling. We find the mass anisotropy always enhance $H_{c2}$ while theZeeman interaction suppresses $H_{c2}$. As required by the thermodynamics, wefind $H_{c2}$ is saturated at zero temperature. We compare the theoreticalcalculations with recent experimental data ofYBa$_{2}$Cu$_{3}$O$_{7-+AFw-delta}$.Comment: To appear in PRB in Feb. 200

Competing effects of mass anisotropy and spin-Zeeman coupling on the upper critical field of a mixedd- ands-wave superconductor