This paper proposes two solutions for the inverse kinematic problem of an industrial parallel robot: a closed analytical form and a Deep Learning approximation model based on three different networks. The analytical form is found and compared against the three Neural Network models: MLP (Multi-Layer Perceptron), deep LSTM (Long-Short Term Memory) and GRU (Gated Recurrent Unit) networks. Algorithms based on these three machine learning (ML) techniques were implemented in a tensorflow environment, using a Deep Learning server machine. Analysis of inverse kinematics is complex and in most cases it pursues multiple solutions; furthermore, an analytic solution exists only for an ideal robot model when the structure of the robot meets certain conditions. Therefore, soft-computing alternatives, along with the Deep Learning concept are qualified candidates due to decreased calculation and processing times compared with other conventional methods. The solution proposed here includes a prediction accuracy comparison between three ML techniques, as well as the validation with the nominal kinematic model of the parallel industrial robot. It is a novel alternative for solving and validating parallel robot models.