Atherosclerosis is a leading cause of heart diseases and mortality around the world. Recently, cryoplasty has emerged as a potential alternative method to treat arterial atherosclerosis. Finite element heat transfer and mass transfer models are developed using ANSYS in this study. The model analyzes the heat transfer within the atherosclerotic plaque and arterial wall during the cryoplasty procedure. The model is useful in predicting the transient temperature through the diseased wall tissues. The results may be used to decide required treatment procedure to effectively freeze the plaque with minimal damage to the healthy arterial tissues. Finally, the model investigates the parameters that may effect temperature distribution within the tissues during the ablative procedure.