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We consider the incompressible Stokes equations in primal velocity–pressure variables and present the mortar finite element formulation for this problem. The local approximation within each subdomain is designed using divergence stable hp‐mixed finite elements. The velocity is computed in a mortared space while the pressure is not subjected to any constraints across the interfaces. Our computational results show that the mortar finite element method for the Stokes problem satisfies similar rates of convergence as the conforming finite element method, in the presence of various h, pand hpdiscretizations (including the case of exponential hpconvergence over geometric meshes). We also present the numerical results for the Lagrange multiplier when the method is implemented as a mixed method. Copyright © 2002 John Wiley & Sons, Ltd.