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This paper presented a new convenient method for viscoelastic problems which are generally solved through complex Laplace transform. State space equation is derived from the differential form of constitutive equation of linear viscoelastic solid that can be solved by a precise integration method which is used in many fields with the advantages of high precision and convenience. For linear viscoelastic solids and crack, the finite elements program of the precise integration method is developed, which appears to be efficient and precise.