Insurance forecasting is essential for the insurance industry. It provides support for long-term business strategies and can serve as a first-step for planning specific lines of products. In the Brazilian context, insurance forecasting is of special relevance. In the Latin American insurance market, Brazil is the leader in premium, and could become one of the most important insurance centers of the world in the medium- or long-term. SUSEP and CNseg forecast insurance products of the Brazilian market with statistical models. Nevertheless, premium time series exhibit nonstationary and nonlinear behavior. Therefore, the use of machine learning algorithms in the modeling of insurance series is justified, due to the ability of these algorithms in capturing nonlinear and dynamic components, which may be present in those series, without making assumptions about the data generating process. Based on this, this work investigates the use of Echo State neural networks (ESN) and GA-SVR in the forecast of insurance premium of the Brazilian market. The database used in this work was provided by SUSEP and consists of the products Automobiles, Life and Providence. Univariate and multivariate forecasts were made with ESN and GA-SVR for the three aforementioned products. The results show predictive superiority of ESN.