The synthesis and investigation of rare-earth metals carbonitrides under high pressure allows to produce new compounds and find relationship between their structures and properties. Previously it was shown that synthesis under high pressure greatly expands the variety of chemistry of carbides and nitrides with potentially promising properties. Some of reported compounds are recoverable at ambient conditions that emphasizes the significance and potential of this research field. Here we propose to synthesize and solve the crystal structures of novel rare-earth metals trinary compounds Me-C-N (Me = Y, La, Sm, Dy) in the pressure range up to 120 GPa. The initial reagents will be the rare-earth metals dicarbides and loaded N2. The main objectives of this proposal are a synthesis of new rare-earth metals carbonitrides Me-C-N at multimegabar pressure, characterization of their crystal chemistry and compressional behaviour, and search for regularities in their chemistry.