  This paper considers stochastic hybrid stress quadrilateral finite element
analysis of plane elasticity equations with stochastic Young's modulus and
stochastic loads. Firstly, we apply Karhunen-Lo$\grave{e}$ve expansion to
stochastic Young's modulus and stochastic loads so as to turn the original
problem into a system containing a finite number of deterministic parameters.
Then we deal with the stochastic field and the space field by
$k-$version/$p-$version finite element methods and a hybrid stress
quadrilateral finite element method, respectively. We show that the derived a
priori error estimates are uniform with respect to the Lam$\acute{e}$ constant
$\lambda\in (0, +\infty)$. Finally, we provide some numerical results.
