A finite element method is derived for solving equations of the following type \[ - (p(x)u'(x,\omega ))' + (q(x) + r(x)\lambda (\omega ))^2 u(x,\omega ) = f(x,\omega ),\quad 0 \leqq x \leqq l,\] with boundary conditions $u(0,\omega ) \equiv u(l,\omega ) \equiv 0$ where (i) $0 < p \in C^1 [0,l]$; (ii) $q,r \in C[0,l]$; (iii) $f(x,\omega ) = B'(x,\omega )$ is the white noise; (iv) $\lambda (\omega )$ is a standard Gaussian random variable and is independent of $B(x,\omega )$ for all $0 \leqq x \leqq l$. We can think of $(q(x) + r(x)\lambda (\omega ))^2 $ as a random perturbation of the deterministic $q(x)^2 $.The error of the finite element solution is estimated and possible extensions are discussed.