Elemental analysis is of fundamental importance in several scientific domains. Many elemental analysis methods have been developed till date, with particular importance having been given to non-destructive analysis methods. In this paper, we review a novel non-destructive, position-selective, and multi-elemental analysis method for bulk material that utilizes a new type of probe, a negative muon. When a muon is stopped by an atom in a material, muonic X-rays are emitted. Due to the large mass of a muon, the energy of muonic X-rays is very high, and the "X-ray fluorescence analysis" method using a muon can solve the problem of self-absorption in an ordinary method using an electron. Two studies involving quantitative and depth-profiling analysis of archeological artifacts by this method are reviewed in this work. We also discuss the scope for future research using this method.