Abstract: Considering the effects of crack gap and strenghening with Fibre Reinforcement Polymer (FRP) as a viscoelastic combination spring,the equivalent flexural rigidity of the cracked beam bonded with FRP sheet in Laplace transformed domain is presented.By using the standard linear solid viscoelastic constitutive relation and Laplace's transformation method,the explicit analytical solutions in time domain for the bending of the viscoelastic beam with an arbitrary number of cracks and FRP sheet reinforcement are derived.By numerical examples,it is stated that FRP sheet has an weakening influence on the crack effect,and the bending solution is inversely proportional to the slender ratio;Strenghened with AFRP sheet reiforcement,the fluctuation of the crack depth and load have less influence on the cracked beam bending.