  A numerical scheme that incorporates a thermal leakage injection model into a
combined gas dynamics and cosmic ray (CR, hereafter) diffusion-convection code
has been developed. The particle injection is followed numerically by filtering
the diffusive flux of suprathermal particles across the shock to the upstream
region according to a velocity-dependent transparency function that controls
the fraction of leaking particles. We have studied CR injection and
acceleration efficiencies during the evolution of CR modified planar shocks for
a wide range of initial shock Mach numbers, $M_0$, assuming a Bohm-like
diffusion coefficient. The injection process is very efficient when the
subshock is strong, leading to fast and significant modification of the shock
structure. As the CR pressure increases, the subshock weakens and the injection
rate decreases accordingly, so that the subshock does not disappear. Although
some fraction of the particles injected early in the evolution continue to be
accelerated to ever higher energies, the postshock CR pressure reaches an
approximate time-asymptotic value due to a balance between fresh
injection/acceleration and advection/diffusion of the CR particles away from
the shock. We conclude that the injection rates in strong parallel shocks are
sufficient to lead to rapid nonlinear modifications to the shock structures and
that self-consistent injection and time-dependent simulations are crucial to
understanding the non-linear evolution of CR modified shocks.
