This paper studies the maximum achievable rate region of multiple access channels (MAC) for a given blocklength n and a desired error probability ∊. The inner region for the discrete memoryless MAC is approximated by a single-lettered expression I − 1/√n Q inv (V, ∊) where I is associated with the capacity pentagon bounds by Ahlswede and Liao, V is the MAC dispersion matrix, and Q inv is the complementary multivariate Gaussian cumulative distribution region. For outer regions, we provide general converse bounds for both average error probability and maximum error probability criteria, and a single-lettered approximation for the discrete memoryless MAC.