The　dynamic　responses　of　offshore　pipelines　induced　by　J-laying　effects　are　remarkable　and　dominate　the　pipeline　design　and　installation　feasibility　in　practice.　Most　previous　studies　have　focused　on　the　analysis　of　pipeline　installation　on　the　horizontal　seabed.　In　this　paper,　an　extended　J-lay　model　based　on　the　vector　mechanics　principle　is　developed　to　investigate　dynamic　behaviors　of　laying　pipelines　on　the　sloping　seabed.　Two　representative　seabed　slope　types　are　taken　into　account　involving　the　positive　and　negative　slopes.　The　laying　pipeline　is　divided　into　a　sequence　of　mass　particles　linked　by　massless　elements,　and　the　deformations　of　the　elements　and　the　rotations　of　the　particles　are　calculated　to　obtain　the　internal　forces.　The　explicit　central　difference　technique　is　applied　to　solve　the　movement　governing　equations　of　pipeline　particles　by　program　coding.　Two　illustrative　cases　of　a　12-inch　pipeline　being　laid　separately　from　the　horizontal　seabed　to　the　positive　and　negative　sloping　seabed　are　simulated　under　a　random　sea　state.　The　influences　of　seabed　slope　type　and　angle　on　pipeline　responses　are　estimated　quantitatively.　Significant　differences　of　pipeline　behaviors　between　the　positive　and　negative　sloping　seabed　are　observed,　which　offer　very　intuitive　evidences　of　seabed　slope　effects　concerning　deepwater　J-laying　pipelines.