A fast and accurate analysis and synthesis technique for high-gain sub-wavelength 2-D Fabry-Perot leaky-wave antennas (LWA) consisting of two periodic metallodielectric arrays over a ground plane is presented. Full-wave method of moments (MoM) together with reciprocity is employed for the estimation of the near fields upon plane wave illumination and the extraction of the radiation patterns of the LWA. This yields a fast and rigorous tool for the characterisation of this type of antennas. A thorough convergence study for different antenna designs is presented and the operation principles of these antennas as well as the radiation characteristics are discussed. Moreover, design guidelines to tailor the antenna profile, the dimensions of the arrays as well as the antenna directivity and bandwidth are provided. A study on the radiation efficiency for antennas with different profiles is also presented and the trade off between directivity and radiation bandwidth is discussed. Numerical examples are given throughout to demonstrate the technique. A finite size antenna model is simulated using commercial software (CST Microstripes 2009) which validates the technique.