While vertical motion induced by long-term geological loads is often used to estimate the flexural rigidity of the lithosphere, we intend to evaluate the shear rigidity of the lithosphere using horizontal motion. Our approach considers that the rigidity of the lithosphere may be defined as its resistance to horizontal tectonic lateral forces. In this case, a spatial distribution of an effective shear rigidity can be estimated from the analysis of the interseismic velocity fields. We consider the Western United States zone where weakly strained areas (e.g., the Sierra Nevada) are connected with areas of large strain rate (e.g. San Andreas Fault system). By inverting interseismic strain distribution measured by geodetic methods, we infer the effective shear rigidity of the lithosphere. The forward problem is defined using the equations of linear elasticity. The inversion relies on the minimization of the sum of a quadratic measure of the differences between measured and modelled velocity fields. The functional also includes regularization terms for the parameters of the model. The gradient of the functional with respect to the minimization parameters is computed using an adjoint formulation. This permits the treatment of large dimensional minimization problems. Finally, a measure of the uncertainty of our inversion is illustrated through the covariance matrix of the parameters at the optimum. The optimization chart is validated on two synthetic velocity distributions. Then, the effective shear rigidity variations of the Western United States are estimated using the CMM3 interseismic velocities. The inversion displays low effective rigidities along the San Andreas Fault system, the Mojave Desert and in the Eastern California Shear Zone, while rigid areas are found in the Sierra Nevada and in the South Basin and Range. Finally, we discuss the differences between our strain rate and rigidity maps with previously published results for the Western United States.