The solutions of the spherically symmetric, linear, isothermal, and transient viscoelasticity problems via reciprocity theorem have been investigated for a specific material. The integral form of stress-strain relations has been used. The Laplace transform of a viscoelastic state, which is necessary for the integral equation arising as a result of reciprocity theorem, has been derived. This integral equation has been solved by Laplace transform. A sample problem has been solved to test the presented formulation. A numerical application of the analytic solution of this problem has been given.