This paper proposes an alternative criteria of the IrL-optimal criteria for the linear re-gression model with r responses based on the volume of the confidence rectangle.This is referred to as RrL-optimality.The RrL-optimality criterion is invariant with respect to different parame-terizations of the model,and reduces to IL-optimality as proposed by Dette and Obrien (1999) in single response situations.A generalization of Elfvings theorem is proved for the RrL-optimal designs to describe the geometrical characterization of RrL-optimality.An equivalence theorem for RrL-optimality is given and used to verify RrL-optimality of designs,and this is illustrated by two examples.