Analysis of polymer-matrix composite sucker rod systems using finite element methods is performed. Composite sucker rods used in oil production fail mainly due to fatigue loading. In majority of cases, the failure is in the region of the joint where the composite rod and the steel endfitting meet. 2D and 3D Finite Element Analysis and experimental tests are carried out in order to observe the stress distribution and to find the regions of stress concentrations inside the endfitting. The causes of failure of the composite sucker rods are identified as high transverse compressive stress caused by overloading that results in the crushing of the rod, and high stress concentrations present at the grooves of the endfitting that initiate premature cracks. Based on the result of this study, enhanced design of the composite sucker rod system can be accomplished.