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The break-up of liquid ligaments and formation of droplets are elementary phenomena in multiphase flows which are of high importance in industrial and medical applications. From the numerical point of view, they require proper interface and surface tension treatment. In the present work, we apply Smoothed Particle Hydrodynamics, a meshless approach, to simulate the break-up of a liquid cylinder inside the gaseous phase, i.e. the Rayleigh-Plateau instability. Results obtained in 3D show that even a relatively coarse resolution allows one to predict correctly the size of droplets formed in the process. The detailed analysis of the break-up time in 2D setup implies that a certain level of spatial discretisation needs to be reached to determine this moment precisely.