The integrated energy systems (IESs), composed of deeply interdependent electric power systems (EPSs) and natural-gas systems (NGSs), are expected to play an important role in the transition to low-carbon sustainable energy systems. To facilitate the security assessment of IESs, this paper initially proposes the concept of IES security region. First, The security region of the IES is defined as a set of energy flow injections for which the energy flow equations and security constraints are satisfied. Next, a set of critical points on the boundary of security region is derived from repeated energy flow solutions. After that, based on the critical points, the hyper-plane approximation method is employed to obtain the critical boundaries and further determine the security region. Finally, the effectiveness of the proposed methodology has been verified.