Slug flow is a two-phase flow pattern which is characterized by the periodic presence of packs of liquid and long bubbles in the tube, associated with high pressure-drops and an often undesired intermittency in the system. The development of the slug pattern in horizontal pipes is caused by two reasons: the natural growth of small disturbancies at the interface (by a Kelvin-Helmholtz instability mechanism) or the liquid accumulation at valleys of hilly terrain pipelines with sections of different inclinations. The present work consists of the numerical simulation of the onset of slugging in both situations, as well as the subsequent development of statistically steady slug flow in the pipe. The prediction of the flow is obtained through a one- dimensional formulation based on the Two-Fluid Model. Averaged slug parameters (length, velocity and frequency) are compared with previous numerical studies and experimental correlations avaiable in the literature, and a very satisfactrory agreement is obtained, specially given the simplicity of a one dimensional formulation.