  We study the metric mean dimension of $\Phi$-irregular set $I_{\Phi}(f)$ 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 $I_{\Phi}(f)\cap B(Y,\varepsilon)\cap CR(f)$
are bounded from below by the respective values for class $Y$.
