S-lay　and　J-lay　systems　are　progressively　utilized　for　deepwater　pipeline　installation.　The　paper　presents　a　simple　and　feasible　model　for　the　static　and　dynamic　analysis　of　S-lay　and　J-lay　pipelines.　This　mechanical　model　of　the　laying　pipeline　is　established　by　the　combination　of　the　vector　mechanics　principle　with　the　numerical　technique　based　upon　the　vector　form　intrinsic　finite　element　(VFIFE)　method.　The　internal　forces　resulted　from　element　deformations　and　node　rotations　as　well　as　the　external　forces　due　to　hydrodynamic　loads　and　the　boundary　interactions　are　fully　taken　into　account.　The　movement　governing　equation　of　pipeline　particles　is　solved　by　the　explicit　central　difference　approach　using　program　coding.　Two　numerical　models　of　a　12-inch　pipeline　being　laid　to　1000　m　water　depth　are　created　in　order　to　illustrate　in　detail　the　modeling　process　of　S-laying　and　J-laying　pipeline,　respectively,　and　also　verify　the　feasibility　of　the　VFIFE　model　with　a　reasonable　accuracy　for　deepwater　pipeline　installation.　The　effects　of　wave　height　and　sloping　seabed　on　the　pipeline　responses　are　identified　and　the　noticeable　differences　of　the　pipeline　behaviors　between　the　S-lay　and　J-lay　operation　are　observed.　The　results　offer　a　significant　reference　for　the　installation　design　of　the　offshore　pipeline.　©　2021　Elsevier　Ltd