In this contribution, the propagation and radiation nature of laterally shielded top-open planar waveguides (LShPW) is studied by using a discrete spectrum of parallel-plate waveguide (PPW) TEz and TMz modes. This formulation allows for a simple but precise analysis of the propagation and radiation characteristics associated with the leaky-wave modes which exist in such planar transmission lines. An approximate novel interpretation of the radiation mechanism is also given by describing each PPW mode as an inhomogeneous plane wave. Comparisons with previous works grant the accuracy of the proposed method. Besides, the analytical and rigorous nature of this approach makes it very suitable for the practical analysis and design of leaky-wave antennas, as will be discussed in the second part of this work.