In this paper, we propose, design and analyze reservoir computing with 2-dimensional (2D) active photonic cavities. The active photonic cavity consists of a multilayer structure, containing lightwave-guiding and active layers. The shape of 2D cavity is defined by highly reflective mirrors. The multilayer forms p-i-n diode, and the cavity has large number of electrodes on its top. The active layer realizes photon generation, detection, and amplification by injecting electric current through electrodes. The mirrors bring short-term memory, and leads to random mixtures of lightwave by the cavity shape, resulting in high dimensionality. High reflectance of the mirrors also enables the lightwave oscillation in the cavity, bringing to its lasing operation. This unstable operation near threshold realizes high nonlinearity. The 2D active photonic cavity is scalable by reducing the size and increasing the number of the electrodes. Reservoir computing(RC) with the 2D active cavity works for numerous purposes by changing the arrangement of the electrodes. Performance of the 2D active photonic cavity is analyzed by simulation. RC with the 2D active photonic cavity demonstrates highly accurate waveform recognition with very small number of training data.