According to the shortcoming of traditional sandwich beam theory that the sandwich beam is incompressible in the thickness direction, a new sandwich beam theory is proposed by introducing independent variables in terms of the displacements of top face sheet, middle plane of soft core and bottom face sheet. The displacement of soft core is approximated by a second order polynomial in the thickness direction. Using continuity conditions along the face sheet and soft core, transverse displacement of soft core is obtained. Normal strain and shearing strain of soft core in the thickness direction are also obtained. Based on Hamilton principal, the governing equation of the system is established. Galerkin truncation method was used to solve the governing equation. It was found that (1) the first mode of soft sandwich beam displays that the face sheet and soft core move together in transverse direction and there is no relative deformation between face sheet and soft core, in this case it is consistent with the traditional sandwich beam theory; (2) the second mode of soft sandwich beam shows that the face sheet moves in opposite direction and the middle plane of soft core does not move, so the soft core is in the state of tension or in compression; (3) the third mode of soft sandwich beam displays that the face sheet moves in the same direction and the soft core moves in opposite direction, so the upper part and lower part of soft core are in different state (tension or compression). By researching the modal sharps, mode functions, response of free vibration, the effect of axially moving velocity on frequencies and so on, we can obtain that the incompressible model of sandwich beam is the special form of soft sandwich beam we establish in this paper.