In this study, we address the feasibility and main properties of a positron emission tomograph (PET) based on RPCs. The concept, making use of the converter-plate principle, takes advantage of the intrinsic layered structure of RPCs and its simple and economic construction. The extremely good time and position resolutions of RPCs also allow the TOF-PET imaging technique to be considered.Monte-Carlo simulations, supported by experimental data, are presented and the main advantages and drawbacks for applications of potential interest are discussed. r