Catching a fast flying object is particularly challenging as consists of two tasks: it requires extremely precise estimation of the object’s motion and control of the robot motion. Any small imprecision may lead the fingers to close too abruptly and let the object fly away from the hand before closing. We present a strategy to overcome for sensori- motor imprecision by introducing softness in the catching approach. Soft catching consists of having the robot moves with the object for a short period of time, so as to leave more time for the fingers to close on the object. We use a dynamical systems (DS) based control law to generate the appropriate reach and follow motion, which is expressed as a Linear Parameter Varying (LPV) system. We propose a method to approximate the parameters of LPV systems using Gaussian Mixture Models, based on a set of kinematically feasible demonstrations generated by an off-line optimal control framework. We show theoretically that the resulting DS will intercept the object at the intercept point, at the right time with the desired velocity direction. Stability and convergence of the approach are assessed through Lyapunov stability theory. The proposed method is validated systematically to catch three objects that generate elastic contacts and demonstrate important improvement over a hard catching approach.