Nonperturbative region of effective strong coupling

In the framework of Poincar\'{e} covariant quark model the behavior of running coupling constant $\alpha_{s}\left(Q^{2}\right)$ is considered in $Q < 1 \mbox{GeV}$ region. An analysis was carried out for pseudoscalar and vector mesons with lepton decay constants, masses (obtained from model dependent) and nucleon spin rules required to match their experimental counterparts. Possible behavior of $\alpha_{s}$ with $\alpha_{\mathrm{crit.}}=\alpha_{s}\left(Q^{2}=0\right) \sim 0.65-0.72$ in the case of a frozen regime, which follows from experimental values of lepton decay constant, masses and nucleon spin rules are discussed.