In the present paper we consider the prostate cancer data to study the applications of life time parametric distributions such as exponential, Weibull and two forms of modified Weibull distributions in the presence of competing risks with three causes of failures. We found that all the four life time distributions give good fit to the prostate cancer data and in comparison, the modified Weibull-II distribution fits well. We have also calculated hazard for the causes  and seen that exponential and modified Weibull-I distribution show constant hazard rate. Where as Weibull and modified Weibull-II distributions have increased hazard rate. We have compared the survival curves of Kaplan-Meier and all four distributions and seen that modified Weibull-II distribution survival curve and Kaplan-Meier survival curve coincides.