Let \({\mathcal O}\subseteq\mathbb{Q}_n\) be an arbitrary finitely generated matrix ring over the rationals. The author presents an algorithmic description of the group of units \(U({\mathcal O})\) of this ring. If \(\mathcal O\) is a matrix ring irreducible over the rationals then the ring is a ring with almost solvable endomorphism group whenever the multiplicative group of the centralizer of \(\mathcal O\) in \(\mathbb{Q}_n\) is an almost solvable group. Theorem 5. Assume that \({\mathcal O}=\text{rg}(x_1,\dots,x_r)\), \(r>2\), is a ring reducible over the field of rationals, and the irreducible components of the ring are absolutely irreducible or irreducible over \(\mathbb{Q}\). If the irreducible components have almost solvable endomorphism groups, then the problem of finding generators for the unit group \(U({\mathcal O})\) is an algorithmically solvable problem.