Lately, in orthodontic treatments, the use of transparent aligners for the correction of malocclusions has become prominent owing to their intrinsic advantages such as esthetics, comfort, and minimal maintenance. Attempts at improving upon this technology by varying various parameters to investigate the effects on treatments have been carried out by several researchers. Here, we aimed to investigate the biomechanical and clinical effects of aligner thickness on stress distributions in the periodontal ligament and changes in the tooth’s center of rotation. Dental finite element models comprising the cortical and cancellous bones, gingiva, teeth, and nonlinear viscoelastic periodontal ligaments were constructed, validated, and used together with aligner finite element models of different aligner thicknesses to achieve the goal of this study. The finite element analyses were conducted to simulate the actual orthodontic aligner treatment process for the correction of malocclusions by generating pre-stresses in the aligner and allowing the aligner stresses to relax to induce tooth movement. The results of the analyses showed that orthodontic treatment in lingual inclination and axial rotation with a 0.75 mm-thick aligner resulted in 6% and 0.03% higher principal stresses in the periodontal ligament than the same treatment using a 0.05 mm-thick aligner, respectively. Again, for both aligner thicknesses, the tooth’s center of rotation moved lingually and towards the root direction in lingual inclination, and diagonally from the long axis of the tooth in axial rotation. Taken together, orthodontic treatment for simple malocclusions using transparent aligners of different thicknesses will produce a similar effect on the principal stresses in the periodontal ligament and similar changes in the tooth’s center of rotation, as well as sufficient tooth movement. These findings provide orthodontists and researchers clinical and biomechanical evidence about the effect of transparent aligner thickness selection and its effect on orthodontic treatment.