A slipform paving machine, comprising: a machine frame including first and second side frame members (14, 16), the machine frame being variable in frame width; at least one first side ground engaging unit (40A, 40C) and at least one second side ground engaging unit (40B, 40D), at least one of the ground engaging units being steerable to control a direction of the slipform paving machine; front and rear first side height adjustable supports (44A, 44C) supporting the first side frame member from the at least one first side ground engaging unit; at least one second side height adjustable support (44B, 44D) supporting the second side frame member from the at least one second side ground engaging unit; a mold (52, 54) supported from the machine frame beneath the machine frame and laterally between the at least one first side ground engaging unit and the at least one second side ground engaging unit, the mold being configured to mold concrete into a concrete structure having an upper surface and lateral concrete sides as the slipform paving machine moves forward in an operating direction, the mold being variable in mold width so as to vary a paving width of the concrete structure; at least two three-dimensional stringless reference objects (S1, S2) configured to correspond to positions of at least two points on the machine frame relative to an external reference system; a controller configured to receive input signals corresponding to the positions of the 3D stringless reference objects in the external reference system, the controller being configured to control height adjustment of one or more of the height adjustable supports and to control steering of the at least one steerable ground engaging unit; characterized in that the slipform paving machine further comprises: a width actuator (24, 26, 28, 30) configured to vary the paving width; a width sensor configured to generate a width signal corresponding to a change in the paving width; and the controller being configured to receive the width signal from the width sensor, and the controller being also configured to control the width actuator (24, 26, 28, 30) so that the paving width can be varied as the slipform paving machine moves forward in the operating direction. a machine frame including first and second side frame members (14, 16), the machine frame being variable in frame width; at least one first side ground engaging unit (40A, 40C) and at least one second side ground engaging unit (40B, 40D), at least one of the ground engaging units being steerable to control a direction of the slipform paving machine; front and rear first side height adjustable supports (44A, 44C) supporting the first side frame member from the at least one first side ground engaging unit; at least one second side height adjustable support (44B, 44D) supporting the second side frame member from the at least one second side ground engaging unit; a mold (52, 54) supported from the machine frame beneath the machine frame and laterally between the at least one first side ground engaging unit and the at least one second side ground engaging unit, the mold being configured to mold concrete into a concrete structure having an upper surface and lateral concrete sides as the slipform paving machine moves forward in an operating direction, the mold being variable in mold width so as to vary a paving width of the concrete structure; at least two three-dimensional stringless reference objects (S1, S2) configured to correspond to positions of at least two points on the machine frame relative to an external reference system; a controller configured to receive input signals corresponding to the positions of the 3D stringless reference objects in the external reference system, the controller being configured to control height adjustment of one or more of the height adjustable supports and to control steering of the at least one steerable ground engaging unit; characterized in that the slipform paving machine further comprises: a width actuator (24, 26, 28, 30) configured to vary the paving width; a width sensor configured to generate a width signal corresponding to a change in the paving width; and the controller being configured to receive the width signal from the width sensor, and the controller being also configured to control the width actuator (24, 26, 28, 30) so that the paving width can be varied as the slipform paving machine moves forward in the operating direction. a width actuator (24, 26, 28, 30) configured to vary the paving width; a width sensor configured to generate a width signal corresponding to a change in the paving width; and the controller being configured to receive the width signal from the width sensor, and the controller being also configured to control the width actuator (24, 26, 28, 30) so that the paving width can be varied as the slipform paving machine moves forward in the operating direction.