A simple 2D numerical model for pipeline and riser configuration analyses is presented. The model considers large deformations of the pipe, pipe-seabed contact detection, pipe's interaction with uneven inelastic seabed, environmental loading such as drag forces applied by the ocean currents, water surface level variations and incorporation of buoyancy modules. The solution technique is based on a consistent minimization of the total potential energy of the deformed pipe discretized as a Riemann sum, which results in a system of nonlinear algebraic finite difference equations that is solved in an incremental/iterative manner. At each increment, the total potential energy is being updated, thus accounting for energy dissipation due to irrecoverable plastic deformation of the seabed and according to hydrodynamic drag forces. The whole pipe is treated as a single continuous segment. To demonstrate the method, examples with several riser configurations and pipe-lay scenarios are presented. It is shown how on-bottom unevenness, including pits and hills, incorporation of buoyancy modules and tidal effects can affect pipeline or riser configurations and their internal forces. Results are compared to those obtained with Abaqus and appear to be in an excellent agreement. The model presents simple and time-efficient way to analyze the pipe-lay or riser configurations with various boundary and loading conditions. The proposed model, contrary to commercial packages, which impose using time-consuming Graphical User Interface (GUI), allows for performing the series of analyses for varying geometric and/or material properties, and processing the results in reasonable time by single click.