Characterizing the gap eigenmode of shear Alfvén waves (SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on the on Large Plasma Device (LAPD) (Zhang et al. 2008 Phys. Plasmas 15012103), a linear large plasma device (Gekelman et al. 1991 Rev. Sci. Instrum. 622875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions (Chang 2014 Ph.D Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAWs using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it clearer. Such a spectral gap is obtained for the magnetic field of B0(z)=1.2+0.6cos[2π(z?33.68)/3.63] with 7.74-m magnetic beach. By introducing two types of local defects (corresponding to Eθ(z0)=0 and E′θ(z0)=0 respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of B0(z)=0.2+0.1cos[2π(z?33.68)/3.63] and with only four magnetic mirrors, which are achievable by the LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAWs on the LAPD and other linear plasma devices.