Rate-Splitting Multiple Access (RSMA) has been recently recognized as a more general multiple access technique that overcomes the limiting factors of its predecessors related to the signal decoding complexity and interference management tradeoff. In this paper, we investigate the application of the RSMA technique to facilitate the users’ concurrent offloading to multiple servers in a multi-server Multi-Access Edge Computing (MEC) system. Each user fully offloads different parts of its computation task at the available MEC servers (or a combination of them) using the same frequency band. We aim to minimize the sum of users’ maximum experienced delay among the different MEC servers, stemming from both the offloading and processing, by jointly optimizing their computation task assignment ratios to the servers, their allocated common-message rates, common and private-message transmission powers, and computing resources related to each server. The formulated min-max-sum problem is non-convex, and its optimization variables are highly coupled. By examining its structure, we equivalently transform the problem and further decompose it into two independent sub-problems that separately provide solutions to the radio and computing resource allocation problems. Numerical results show the effectiveness of the proposed solution in terms of the users’ experienced delay and the proposed algorithm’s real execution time.