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In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring $(R,ℳ)$, the following statements are equivalent: (1) Every prime ideal of $R$ is a direct sum of cyclic $R$-modules; (2) $ℳ={⨁}_{\lambda \in \Lambda }R{w}_{\lambda }$ where $\Lambda$ is an index set and $R/Ann\left(w_{\lambda }\right)$ is a principal ideal ring for each $\lambda \in \Lambda$; (3) Every prime ideal of $R$ is a direct sum of at most...