Resistive Random Access Memory (ReRAM) is one of the most promising emerging non-volatile memory (NVM) candidates due to its fast read/write speed, excellent scalability and low-power operation. Recently proposed 3D vertical cross-point ReRAM (3D-VRAM) architecture attracts a lot of attention because it offers a cost-competitive solution as NAND Flash replacement. In this work, we first develop an array-level model which includes the geometries and properties of all the components in the 3D structure. The model is capable of analyzing the read/write noise margin of a 3D-VRAM array in the presence of the sneak leakage current and voltage drop. Then we build a system-level design tool that is able to explore the design space with specified constraints and find the optimal design points with different targets. We also study the impact of different design parameters on the array size, bit density, and overall cost-per-bit. Compared to the state-of-the-art 3D horizontal ReRAM (3D-HRAM), the 3D-VRAM shows great cost advantage when stacking more than 16 layers.