The Smoothed Particle Hydrodynamics or SPH method is a meshless numerical method applicable to various problems in computational fluid dynamics (CFD). It is considered as an alternative to the traditional methods based on Navier-Stokes equations solved on meshes of discrete points. In the SPH method, the fluid is discretized with interacting particles. The SPH model consists of the aproximations of function values (velocity, density, pressure) and their derivatives using the smoothing function. Equations of SPH model are Navier-Stokes equations written for a specific particle. The method can also be used in simulations of multiphase flows where surface tension force can have a major impact. In this master thesis, a SPH method with surface tension force model is presented. Capabilities of the SPH method were demonstrated on two multiphase flow problems, where effects of surface tension force and other model parameters are presented. They also prove that SPH method is truly a powerful tool. First problem is deformation of a square droplet and the second one is famous Rayleigh-Taylor instability.