The control of flexible robot manipulators is a challenging task, especially when one considers parallel and interconnected manipulators under flexibility considerations. This paper proposes a method to estimate the position of the end-effector of a flexible interconnected manipulator based on a virtual sensor principle and function approximation schemes. By using SolidWorks/MSC ADAMS software, we developed a virtual prototype of a flexible interconnected manipulator, and rigorously evaluated the feasibility of using function approximation schemes such as Neural Networks (NN), Support Vector Machines (SVM), and Gaussian Process (GP) in estimating the deflection error arising due to the flexibility of the robot structure. Our rigorous computational experiments have shown that: (1) the NN, SVM, and GP models were are able to attain the promising and reasonable prediction accuracy, (2) a feedforward NN with 535 neurons and an Ascending distribution of its nodes achieves the best prediction and generalization to unseen environments (the upper bound of the error was 0.15 × 10−3 m); implying the robust estimation of the position of the end-effector under flexibility considerations, and (3) the control based on the inverse Jacobian and a NN-based estimator was able to follow a sinusoidal trajectory with reasonable tracking and error performance in MSC ADAMS & MATLAB/Simulink co-simulation. Our results show the feasibility and effectiveness of the nonlinear relationships learned by NN, SVM, and GP in aiding estimation and control of the position of the end-effector of the flexible manipulator with a promising/desirable capability.