In this paper, we consider the inextensible flows in semi-Euclidean 4-space with index $2$ ($\mathbb{E}_{2}^{4}$). We give the necessary and sufficient conditions for the flow to be inextensible and we find the evolution equations for the inextensible flows in semi-Euclidean $4$-space with index 2 ($\mathbb{E}_{2}^{4}$).