Progressing Cavity Pumps (PCP) are positive-displacement pumps customarily employed in the petroleum industry for artificial lift of high viscosity oils, or fluids with moderate degree of gas and/or sediments. Basically, an elastomeric PCP consists of a metallic helical rotor and a twin helix rubber stator. For this kind of PCP, flow is strongly modified by structural deformations undergone by the stator. For automation, design and operation optimization purposes, any mathematical model able to accurately describe and predict flow and structural phenomena inside these pumps is welcome. However, due to its intrinsically coupled non-linear multiphysics - flow and structural fields, friction, wear, heat generation - analysis of the real dynamic interaction is very complex and experimental measuring is extremely hampered by the elastomeric nature of the stator. Therefore, as an attempt to describe and numerically evaluate this dynamic behavior, the present work features a simplified three-dimensinoal computational model for analysis of the fluid-structure interaction (FSI) in single-lobe elastomeric progressing cavity pumps. The governing unsteady and three-dimensional fluid dynamic equations, for laminar or turbulent flow, are solved using an Element-based Finite Volume Method in a moving and deformable mesh, to account for the relative motion between rotor and stator, and the stator deformation as well. Once a pressure distribution on the stator inner surface is obtained, for an initial non-deformable fluid domain/geometry, it is then used to evaluate the corresponding structural deformations of the elastomeric stator. In the present model, only radial deformations are allowed, being explicitly evaluated following an elastic linear model. This procedure is continuously repeated until "converged" geometrical configuration and flow field are reached before a new time step is advanced. In addition to dynamically provide detailed information on flow and structural fields (pressure, velocity, deformation and tension distributions), operational parameters such as volumetric efficiency, viscous loses and torque, for example, are precisely predicted by the model developed as function of several parameters (rotor and stator dimensions, pump rotation and differential pressure, fluid viscosity, and elastomer bulk modulus). Numerical results are presented and compared against experimental findings, illustrating the behavior of the main fields, for the different governing parameters.