Metric mean dimension of irregular sets for maps with shadowing

We study the metric mean dimension of $\mathrm{\Phi }$-irregular set $I_{\mathrm{\Phi }}(f)$ in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class $Y$, the values of topological entropy together with the values of lower and upper metric mean dimension of the set $I_{\mathrm{\Phi }}(f)\cap B(Y,\epsilon )\cap CR(f)$ are bounded from below by the respective values for class $Y$.