First birth interval is one of the examples of survival data. One of the characteristics of survival data is its observation period that is fully unobservable or censored. Analyzing the censored data using ordinary methods will lead to bias, so that reducing such bias required a certain method called survival analysis. There are two methods used in survival analysis that are parametric and non-parametric method. The objective of this paper is to determine the appropriate method for modeling the birth of the first child. The exponential model with the inclusion of covariates is used as parametric method, considering that the newly married couples tend to have desire for having baby as soon as possible and such desire will be weakened by increasing age of marriage. The data that will be analyzed were taken from the Indonesia Demographic and Health Survey (IDHS) 2012. The result of data analysis shows that the birth of the first child data is not exponentially distributed thus the Cox proportional hazard method is used. Because of the suspicion that disproportional covariate exists, then the proportional hazard test is conducted to show that the covariate of age is not proportional, the generalized Cox proportional method is used, namely Cox extended that allows the inclusion of disproportional covariates. The result of analysis using Cox extended model indicates that the factors affecting the birth of the first child in Indonesia are the area of residence, educational history and its age.