Performing a survival analysis, allows investigating factors that contribute to outcome over time. Though a considerable amount of literature has addressed this area, analysis of multiple survival responses has not received sufficient attention in past literature. The joint modeling fits well when there are multiple survival responses for the same study unit and it can provide improved results than fitting univariate models separately since the correlation between the responses can be captured through a joint model. Therefore, the aim of this study was to propose a joint modeling approach, in which the linkage between two survival responses(for simplicity, in this research bivariate lifetime data have been considered) was derived by sharing a common random effect under different random effect distributions through parametric forms of the baseline hazard function. In this study, Gamma and Normal random effect distributions and Exponential and Weibull parametric survival distributions were considered. The performance of the Shared Frailty model was compared with two Ordinary Proportional Hazard models through a simulation study, by fitting models for simulated data in three different sample sizes with 20% and 40% censoring proportions in different correlation structures. Bias, Coverage Probability (CP) and Mean Squared Error (MSE) were the performance measures used. Parameter estimates showing relatively low bias, high CP, and minimal MSE under the joint random effect model confirmed the suitability of the proposed model to capture joint survival data, surpassing the fit of two univariate models. Also, the results interpreted, Gamma distributed random effects to be more suitable with Exponential survival times while Normal random effects with Weibull survival times.