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A computational procedure is presented for the solution of frictionless contact problems of aircraft tires. The space shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters, transverse shear deformation, and geometric nonlinearities included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The elemental arrays are obtained by using a modified two-field mixed variational principle. Numerical results are presented for the shuttle nose-gear tire when subjected to inflation pressure and pressed against a rigid pavement. Comparison is made with the experiments conducted at NASA Langley.