This paper focuses on facility layout problems with shape constraints. A heuristic algorithm is developed for the problems with the objective of minimizing the sum of rectilinear distances weighted by flow amounts between the facilities. The suggested algorithm is a simulated annealing algorithm in which a solution is encoded as a matrix that has information about relative locations of the facilities on the floor. A block layout is constructed by partitioning the floor into a set of rectangular blocks according to the information while satisfying the areas of the facilities. In this paper, three methods are suggested for the partitioning procedure and they are employed in the simulated annealing algorithm. The results of computational experiments show that the proposed algorithm performs better than two existing algorithms.