Covalent-organic-frameworks (COFs) are crystalline porous polymers with periodic skeleton that assembled from diverse building blocks that attracted increasing interest due to their high designability and porosity, which show potential applications in many areas, such as gas separation, organic opto/electronics, membrane filtration and energy storage/conversion. However, much attention was only focusing on structural designs and preparation methods towards their functional utilizations, and very limited work had been reported on their mechanical properties which play critical roles in practical applications. Considering its two-dimensional nature and covalently bonded skeleton, 2D COFs are envisioned to process outstanding mechanical properties, and distinct from inorganic 2D materials such as graphene and MoS2, which are strong yet brittle as they lack sufficient interlayer interaction, COFs can be designed and synthesized with molecular level control, By rational design monomers, we can control the skeleton of 2D COFs, such as the pore size and pore shape, as well as the surface chemistry that can form strong interactions between layers, which provide an exciting platform to control the membrane mechanical properties at diverse dimensional. The objection of this thesis is to develop a systematic study of the mechanical properties of COF membranes. Specific Aim 1 is to perform in-situ tensile test under SEM and investigate the crack propagation in porous 2D COF membranes (Chapter 2). Specific Aim 2 is to rationally design the monomer to enhance the interlayer interaction between COF adjacent layers, and further study how hydrogen bonds affect the mechanical properties of multilayer COF membranes (Chapter 3). Specific aim 3 is to prepare 2D COF by a vapor phase method and study its mechanical and electronic properties, and its heterostructure with transition metal dichalcogenides are also studied(Chapter 4). This thesis provided systemic investigation on the synthesis, characterization of 2D COFs and the potential application of 2D COFs in nanoelectronics.