The rigid modal of free beam on inhomogeneous Winkler foundation or doubleparameter foundation relates to the interaction between beam and soil. When there is no constraint or the existent constraints don't influence beam's translation or rotation, the corresponding rigid modal will occur. In order to consider the effect of soil under and around the beam, doubleparameter foundation model was introduced. Based on Hamilton principle and calculus of variation, the vibration equation of beam on doubleparameter foundation was deduced, and the variable regularity of modal frequency and modal shape with the inhomogeneous foundation were analyzed.