A number of studies have been made on the parallelism embedded in the logic programming languages for the purpose of performance improvements in the execution of the logic programs. The difficulty of AND parallel execution is due to the shared variables between the subgoals. This problem can be resolved by the algorithm that controls which subgoal is solved first. The algorithm can be used either at compile-time or at run-time. The proposed model is applied to the tree-structured architecture, using the allocation algorithm which allocates the clauses to be unified with each subgoal of a clause to the child processors of the current processor which contains that clause.