It has been discovered that any RNA can be targeted for cleavage by RNAase P from eukaryotic cells, for example, human RNAase P, using a suitably designed oligoribonucleotide ("external guide sequence", or EGS) to form a hybrid with the target RNA, thereby creating a substrate for cleavage by RNAase P in vitro. The EGS hydrogen bonds to the targeted RNA to form a partial tRNA like structure including the aminoacyl acceptor stem, the T stem and loop, and part of the D stem. The most efficient EGS with human RNAase P is the EGS in which the anticodon stem and loop was deleted. Modifications can also be made within the T-loop. Methods are also disclosed to randomly select and to express a suitable EGS in vivo to make a selected RNA a target for cleavage by the host cell RNAase P, thus preventing expression of the function of the target RNA. The methods and compositions should be useful to prevent the expression of disease-causing genes in vivo.