The critical flow velocity for a horizontal clamped-clamped pipe conveying two-phase flow is investigated. The system is represented by a coupled fluid-structure fourth-order Partial Differential Equation (PDE). In the case of the multiphase flow, the no-slip homogeneous flow is adopted. The PDE is transformed to a set of first-order ODEs using both Galerkin and state-space methods. The final system of equations represents an eigenvalue problem, where the eigenvalues are the natural frequency of the system. Specialized software has been employed to solve it. Results of critical flow velocity of gas as a function of homogeneous void fraction (fraction of the transversal area occupied by the gas) are presented representing a velocity stability map. The later suggest that the critical flow velocity increases with increasing the homogeneous void fraction.