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Let A be a commutative ring and I an ideal of A. The amalgamated duplication of A along I, denoted by $${A \bowtie I}$$ , is the special subring of $${A \times A}$$ defined by $${A \bowtie I } := \pi \times_{\frac{A}{I}} \pi = \{(a, a + i) \mid a \in A, i \in I\}$$ . We are interested in some basic and homological properties of a special kind of $${A \bowtie I}$$ -modules, called the duplication of M along I with M is an A-module, and defined by $${M \bowtie I := \{(m, m') \in M \times M \mid m - m^{\prime} \in IM\}}$$ . The new results generalize some results on amalgamated duplication of a ring along an ideal. [ABSTRACT FROM AUTHOR]