  We present a formalism for rigorous calculations of cross sections for
inelastic and reactive collisions of ultracold atoms and molecules confined by
laser fields in quasi-2D geometry. Our results show that the
elastic-to-inelastic ratios of collision cross sections are enhanced in the
presence of a laser confinement and that the threshold energy dependence of the
collision cross sections can be tuned by varying the confinement strength and
external magnetic fields. The enhancement of the elastic-to-inelastic ratios is
inversely proportional to $\sqrt{\epsilon/\hbar \omega_0}$, where $\epsilon$ is
the kinetic energy and $\omega_0$ is the oscillation frequency of the trapped
particles in the confinement potential.
