An apparatus for vertical slip forming of concrete structure on a base comprising a slipform assembly connected through a formwork frame to an attachment portion, wherein the slipform assembly comprises an extrusion form providing mould walls defining a cavity with a top open surface and a bottom open surface and first actuators (140, 240, 152) adapted to adjust the position of the mould walls (81, 82, 181, 182), essentially arranged along the longitudinal axis of the slipform assembly, during the incremental vertical movement of the slipform assembly relative to the frame; concrete supply means connected with the slipform assembly for delivering concrete (52, 53, 54) to that cavity through the top open surface; and second actuators, connected to said attachment portion, for vertically displacing that slipform assembly incrementally relative to the base thereby to continuously or incrementally cast a concrete structure having a vertical orientation, wherein said second actuators are adapted to adjust the position of the formwork frame and the mould walls as such and in their entirety during the incremental vertical movement of the slipform assembly relative to the base by displacing the bottom open surface of the slipform assembly laterally offset from the initial position of said bottom open surface of the slipform during the incremental vertical movement and/or by rotating the slipform assembly relating to the longitudinal direction of the extrusion process in parallel to the incremental vertical movement and/or by tilting the slipform assembly relating to the longitudinal direction of the extrusion process in parallel to the incremental vertical movement, characterized in that either the mould walls comprise an inner wall surface provided with a foil, and wherein the first actuators (140, 240) are adapted to adjust the position of the mould walls (81; 181) during the incremental vertical movement of the slipform assembly relative to the frame by moving portions of the mould walls independently from other portions of the mould walls in a perpendicular direction relating to the longitudinal direction of the extrusion process in parallel to the incremental vertical movement through displacing the foil from the inner wall surface of the slipform mould walls to provide different cross section forms of the inner cavity near the bottom surface, in parallel to the incremental vertical movement, or the mould walls of the slipform assembly are cylindrical forming a cylindrical tube with a circular bottom surface and wherein the first actuators are adapted to change the diameter of the circular bottom surface, especially parallel in time to the incremental vertical movement of the slipform assembly relative to the frame. characterized in that either the mould walls comprise an inner wall surface provided with a foil, and wherein the first actuators (140, 240) are adapted to adjust the position of the mould walls (81; 181) during the incremental vertical movement of the slipform assembly relative to the frame by moving portions of the mould walls independently from other portions of the mould walls in a perpendicular direction relating to the longitudinal direction of the extrusion process in parallel to the incremental vertical movement through displacing the foil from the inner wall surface of the slipform mould walls to provide different cross section forms of the inner cavity near the bottom surface, in parallel to the incremental vertical movement, or the mould walls of the slipform assembly are cylindrical forming a cylindrical tube with a circular bottom surface and wherein the first actuators are adapted to change the diameter of the circular bottom surface, especially parallel in time to the incremental vertical movement of the slipform assembly relative to the frame.