We investigate properties of group gradings on matrix rings 𝑀𝑛⁡(𝑅), where R is an associative unital ring and n is a positive integer. More precisely, we introduce very good gradings and show that any very good grading on 𝑀𝑛⁡(𝑅) is necessarily epsilon-strong. We also identify a condition that is sufficient to guarantee that 𝑀𝑛⁡(𝑅) is an epsilon-crossed product, i.e. isomorphic to a crossed product associated with a unital twisted partial action. In the case where R has IBN, we provide a characterization of when 𝑀𝑛⁡(𝑅) is an epsilon-crossed product. Our results are illustrated by several examples.