One of the main concerns in archaeology is to find of a method to study precisely archaeological structures in the least invasive way possible to avoid damage. The requirement of preserving the structures integrity prevents, in the case of pyramids or tumuli, the study of any internal structure (halls or tombs) which are not reachable by existing corridors.One non-invasive method is the muontomography. By placing a detector which allows to register the muon direction after the structure, it is possible to have an idea of its composition based on the attenuation of the muon flux, which depends on the material length and density that muons have crossed. This technique, alone or together with other exploration techniques as seismictomography or electrical resistivitytomography, can provide useful information about the internal structure of the archaeological form that can not be obtained by conventional archaeological methods.In this work, the time measurement necessary to obtain a significant result about the composition of an archaeological structure is estimated. To do that, a Monte Carlo simulation framework based on the MUSIC software, properly tuned for this study, has been developed. The particular case of the Kastas Amfipoli Macedonian tumulus has been considered to perform the simulations.