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We explore a linear inhomogeneous elasticity equation with random Lam\'eparameters. The latter are parameterized by a countably infinite number ofterms in separated expansions. The main aim of this work is to estimateexpected values (considered as an infinite dimensional integral on theparametric space corresponding to the random coefficients) of linearfunctionals acting on the solution of the elasticity equation. To achieve this,the expansions of the random parameters are truncated, a high-order quasi-MonteCarlo (QMC) is combined with a sparse grid approach to approximate the highdimensional integral, and a Galerkin finite element method (FEM) is introducedto approximate the solution of the elasticity equation over the physicaldomain. The error estimates from (1) truncating the infinite expansion, (2) theGalerkin FEM, and (3) the QMC sparse grid quadrature rule are all studied. Forthis purpose, we show certain required regularity properties of the continuoussolution with respect to both the parametric and physical variables. To achieveour theoretical regularity and convergence results, some reasonable assumptionson the expansions of the random coefficients are imposed. Finally, somenumerical results are delivered.

Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties