Given a set Q of squares with positive profits, the square packing problem is to select and pack a subset of squares of maximum profit into a rectangular bin R\mathcal R . We present a polynomial time approximation scheme for this problem, that for any value ε> 0 finds and packs a subset Q′ ⊆ Q of profit at least (1 − ε) OPT, where OPT is the profit of an optimum solution. This settles the approximability of the problem and improves on the previously best approximation ratio of 5/4 + ε achieved by Harren’s algorithm.