Abstract This article examines a kinematic model of a group pursuing several targets by the method of parallel approach. The model is based on the fact that pursuers try to adhere to pre-designed trajectories. The pursuers’ trajectories have curvature constraints. The initial directions of the pursuers’ velocities are arbitrary, which changes the well-known method of parallel approach. In our model, targets are chased by the pursuers simultaneously. This is due to the change in the lengths of the predicted trajectories in such a way as to synchronize the time to reach the target. The change in the lengths of the predicted trajectories occurs due to an increase in the radius of curvature in the initial segment of the trajectory.