An improved version of a numerical method for computing collision probabilities is developed for r--z geometry. It is concluded from the results of numerous test cases that the method can be used to compute collision probabilities in this geometry with an accuracy better than 0.1% in typically <1 s (occasionally, in a few seconds when dealing with difficult cases) on the Athlon 64 3200+ processor. The developed algorithm is implemented into the framework of the collision probability method and tested for one-group criticality problems for finite circular and semicircular cylinders.