This paper conducts survival analysis on the kidney transplant-related data collected by United Network for Organ Sharing (UNOS) since 1987. We investigate which kidney transplant-related variables from UNOS have significant effect on recipients' survival time and the extent of the effects. Standard Cox Proportional-Hazards model, Cox-Proportional Hazards model with ridge, LASSO and elastic net penalty and lastly random survival forest model are used to compute the survival function after kidney transplantations, which we use to estimate patients' survival probability at time t of a given transplant. Length of stay(LOS) at the hospital after transplant comes out to be the most significant variable in determining patient's survival probability. The longer the patient stayed post transplant, the higher the survival probability. Following the modeling, we compare these models based on two different scores: concordance index and the brier score. Concordance index checks whether the models generate reliable ranking of survival times(i.e. discrimination), while the brier score calculates the average squared distances(i.e. calibration). Random Survival Forest model provides the best result based on the brier score, while Kaplan-Meier model produces the best outcome based on the concordance index.