The study of well control is critical to determine the main variables involved in well drilling and construction operations. The analysis of these operations aims to establish important parameters that must be followed in order to avoid an influx of fluids from the formation into the well (kick). In order to guarantee safety during drilling operations, the hydrostatic pressure at the bottom of the well must be greater than the formation pore pressure. This work presents a mathematical modeling, developed to simulate a water and oil kick from the formation that enters a vertical onshore well and, thus, predict the pressure behavior inside the production string and the annular space during a well control situation. The control operation is composed of the kick inflow, well closure and expulsion of the invading fluid. The gas kick case was not assessed because of its complexity. The studied model has been simulated in Visual Basics, in Excel, using the characteristics method with finite difference formulation. Considerations were taken about the effect of well geometry, friction loss, influx expansion and two phase flow model.