The S-lay method has been widely used in pipeline installation from shallow water to deep water for decades. In this paper, a novel numerical model for analyzing pipelines in the S-lay problem is proposed to investigate the overall configuration, internal forces, and strain of the pipeline taking into account the influence of ocean currents and seabed stiffness. The influence of many important factors, including the variation position of the liftoff point, the change of stinger radius, ocean currents, seabed stiffness are investigated in detail. Some useful results are obtained: the stress state of the pipeline is found to vary greatly during the whole laying process; the train of the pipeline at both the upper and the lower sides is very important; ocean currents have negligible influence on the pipeline; traditional “touchdown factor” is not suitable to predict the real pipe embedment; and soil stiffness plays an important role in pipeline behavior on the seabed. The illustrative examples and comparison with a previous work demonstrate the widespread applicability of this model. Moreover, the solution process of this model is easy and fast, so it is suitable for engineering applications.