For a tree T rooted at a concentrator location in a telecommunication system, we assume that the capacity H for the concentrator is given and a profit $c_v$, and a demand $d_v$, on each node $upsilon$ of T are also given. Then, the capacitated subtree of a tree problem (CSTP) is to find a subtree of T rooted at the concentrator location so as to maximize the total profit, the sum of profits over the subtree, under the constraint satisfying that the sum of demands over the subtree does not exceed H. In this paper, we develop a pseudopolynomial-time algorithm for CSTP, the depth-first dynamic programming algorithm. We show that a CSTP can be solved by our algorithm in $ heta$ (nH) time, where n is the number of nodes in T. Our algorithm has its own advantage and outstanding computational performance incomparable with other approaches such as CPLEX, a general integer programming solver, when it is incorporated to solve a Local Access Telecommunication Network design problem. We report the computational results for the depth-first dynamic programming algorithm and also compare them with those for CPLEX. The comparison shows that our algorithm is competitive with CPLEX for most cases.