This paper uses the structural time series models to analyze U.S. Birth data (from 1946 to 2017) and U.S. Population data (from 1946 to 2018). Main focus is to study what kind of the stochastic structures that U.S. Birth and U.S. Population can be fitted. This paper uses the local level model, fixed trend model and local linear trend model. With the state space form of these three models, the Kalman filter is used to estimate unknown parameters, to predict one step ahead data and to do filtering data. Based on the AIC and validity check, the best fitted models for U.S. Birth and Population are recommended.