We consider color-screening effects in soft hadron-hadron and hadron-nucleus collisions at high energies using the idea of constituent (or dressed) quarks. It is shown that the quark color-screening hypothesis can be formulated as a sum rule for the elastic and inelastic quark-quark amplitudes. Taking into account color-screening effects, the cross sections ${\ensuremath{\sigma}}_{\mathrm{tot}}$ and $\frac{d{\ensuremath{\sigma}}_{\mathrm{el}}}{\mathrm{dt}}$ are calculated for hadron-hadron and hadron-nucleus collisions.