Trapping of obliquely incident surface waves by permeable flexible barriers placed near a vertical rigid wall in a two-layer fluid having free surface and an interface is studied for both surface-piercing and bottom-standing partial barriers. For the surface-piercing permeable flexible barrier, the barrier is assumed to be fixed near the free surface and is free at the submerged end. On the other hand, for the bottom standing permeable flexible barrier, the barrier is assumed to be fixed at the bottom and the other end is free. As special cases of the permeable flexible barrier, the results associated with surface-piercing and bottom-standing permeable membrane barriers are obtained by assuming that the two ends of the barriers are fixed. Appropriate continuity conditions are used to deal with the interface-piercing flexible/membrane barriers. The mathematical problem is handled for solution using a generalized orthogonal relation suitable for two-layer fluid along with the least square approximation method. Explicit relations are derived to ensure full reflection by porous flexible barriers of any configuration placed near a vertical rigid wall for waves in surface and internal modes, which are validated through numerical computations in various cases. The effect of critical angle of incidence on wave reflection and trapping by barriers, surface and interface wave elevations, deflection of the flexible barrier under wave action, pressure distribution on the barrier, wave loads on barrier and rigid wall are analyzed. The finding of the present study is likely to play a significant role in the design of marine facilities with less wave force on the infrastructure. The present concept and methodology can be easily extended to similar problems in acoustic-structure interactions.