Let \(k\) be an algebraically closed field of characteristic \(p>3\) and \({\mathcal W}_l = \{\partial_i,x_i: [\partial_i, \partial_j] = [x_i,x_j]=0\), \([\partial_i,x_j] = \delta_{i,j}\),, \(j=1,2, \dots, l\}\) be the Weyl algebra over \(k\). Let \(m\) be an \(l\)-tuple of positive integers and \(b\) an \(l\)-tuple of non-zero elements of \(k\) and \(a\) any \(l\)-tuple of elements of \(k\). Denote by \({\mathcal P} (m,a,b)\) the representation of \({\mathcal W}_l\) on the vector space \(k[x_1,\dots,x_l]/(x_1^{p^{m_1}}-b_1,\dots,x_l^{p^{m_l}}-b_l)\) defined by setting \(x_ix^n=x^{n+\varepsilon_i}\), \(\partial_ix^n = b_i^{-1} (n_i+a_i)x^{n+(p^{m_i}-1) \varepsilon_i}\), where \(n=(n_1, \dots, n_l)\), \(x^{\varepsilon_i} = x_i\). The Weyl algebra \({\mathcal W}_l\) has subalgebras isomorphic to classical Lie algebras of types \(A_{l-1}\) and \(C_l\). In the paper restrictions of the \({\mathcal W}_l\)-module \({\mathcal P} (m,a,b)\) to these subalgebras are considered. These representations include a class of pointed torsion free representations, a class of irreducible nonrestricted representations, and a class of indecomposable representations of arbitrary higher dimension. Irreducible representations of the modular Weyl algebra are classified.