The pneumatic tire is treated as a laminated, anisotropic, toroidal shell of revolution possessing bending rigidity. The plies, which are constructed of elastic textile cords embedded in an elastic rubber matrix, are considered homogeneous and orthotropic on a macroscopic scale. The tire shell is considered to deform according to the classical Love hypothesis. The equilibrium, strain‐displacement, and laminate constitutive equations governing the tire shell are reduced to a system of six first order, nonlinear, ordinary differential equations with variable coefficients which are solved numerically by a multi‐segment forward integration technique. The geometrical nonlinearities due to finite displacements are accounted for by an incrementing process using transient coordinates. The theory is illustrated by a numerical calculation which shows good agreement with actual measurements.