A new class of partitions, partitions with designated summands, was introduced by Andrews, Lewis and Lovejoy. Let e64547d495ce7a391" title="Click to view the MathML source">PD(n) denote the number of partitions of n with designated summands. Andrews, Lewis and Lovejoy established many congruences modulo 3 and powers of 2 for e64547d495ce7a391" title="Click to view the MathML source">PD(n) by using the theory of modular forms. In this paper, we prove several infinite families of congruences modulo 9 and 27 for e64547d495ce7a391" title="Click to view the MathML source">PD(n) by employing the generating functions of PD(3n) and PD(3n+1) which were discovered by Chen, Ji, Jin and Shen. For example, we prove that for e62883d5bc5921f92de6ffae358e" title="Click to view the MathML source">n≥0 and e639e59033edb2058424b" title="Click to view the MathML source">k≥1, e699784c019f9ac7c">. Furthermore, using some results due to Newman, we find some strange congruences modulo 27 for e64547d495ce7a391" title="Click to view the MathML source">PD(n). For example, we prove that for k≥0, and , where p is a prime and .