Numerical kinetic code capable to integrate the dynamical collisional kinetic equation has been developed. The steady state distribution of ions in a mirror cell with flow-through plasmas has been calculated. It has shown that near separatrix there is a phase-space region with unstable inverted gradient of the distribution function. The dispersion relation of the oscillations with ~ b (b is bounce-frequency of ions) has been treated analytically for simplified model with b = const. Interaction of passing ions with the oscillations has been considered. It is found that passing ions could lead to instability as long as their flow velocity is high enough.