Machines may not be available all the time due to uncertain breakdown or preventive maintenance activities. In this paper we develop a branch and bound algorithm to solve the flexible flowshop scheduling problems with non-resumable availability constraint. Both the machine-based and job-based lower bounds are developed by making use of the lower bounds of the classical flexible fowshop problems. Numerical experiments are conducted and the results show that the branch and bound algorithm is effective when the problem size is not very large.