Collisions, resulting in aggregation of ice crystals in clouds, is an important step in the formation of snow aggregates. Here, we study the collision process by simulating spheroid-shaped particles settling in turbulent flows and by determining the probability of collision. We focus on platelike ice crystals (oblate ellipsoids), subject to gravity, and to the Stokes force and torque generated by the surrounding fluid. We also take into account the contributions to the drag and torque due to fluid inertia, which are essential to understand the tendency of crystals to settle with their largest dimension oriented horizontally. We determine the collision rate between identical crystals, of diameter 300 μ m, with aspect ratios in the range 0.005 ≤ β ≤ 0.05, and over a range of energy dissipation per unit mass, ε , 1 ≤ ε ≤ 250 cm 2 s −3 . For all values of β studied, the collision rate increases with the turbulence intensity. The dependence on β is more subtle. Increasing β at low turbulence intensity (ε <≈ 16 cm 2 s −3) diminishes the collision rate, but increases it at higher ε ≈ 250 cm 2 s −3 . The observed behaviors can be understood as resulting from three main physical effects. First, the velocity gradients in a turbulent flow tend to bring particles together. In addition, differential settling plays a role at small ε when the particles are thin enough ( β small), whereas the prevalence of particle inertia at higher ε leads to a strong enhancement of the collision rate.