This paper describes the design and the experimental validation of a multivariable shape controller for the JET tokamak. This new controller allows the control of extremely shaped plasmas with high values of elongation and triangularity. The problem has been formulated as an output regulation problem for an LTI plant whose controllable outputs are more than the control inputs. For the case of constant references, we propose a control scheme which minimizes a quadratic cost function. This cost function weights the tracking error at steady-state. Our methodology is based on the singular value decomposition of the static gain matrix of the plant. In the controller design we also take into account the steady-state control effort. Some experimental results are presented.