An exact symplectic approach is presented for the isotropic viscoelastic solids subjected to external force and temperature boundary conditions. With the use of the method of separation of variables, all the general solutions of the governing equations are derived in the Laplace domain. These general solutions are expressed in concise analytical forms, and are easily to be transformed into the time domain. Accordingly, various boundary conditions can be conveniently described by the combination of the general solutions due to the completeness of the solution space. In the numerical example, the whole character of total creep of the viscoelastic solid is clearly exhibited.