Investigations by powder X-ray diffraction, susceptibility measurements and neutron diffraction experiments on the ternary silicides RCoSi (R = La-Sm, Gd, Tb) are reported. They crystallize in the tetragonal structure of the CeFeSi type (space group P4/nmm). This structure is closely related to the ThCr2Si2 structure and can be described as isolated ''ThCr2Si2 blocks'' (''BaAl4 slab'') connected via R-R contacts. LaCoSi is a Pauli paramagnet while CeCoSi and PrCoSi are Curie-Weiss paramagnets down to 1.6 K. The other compounds (Nd, Sm, Gd, Tb) are antiferromagnetic below T(N) = 7(1) K, 15(3) K, 175(3) K and 140(3) K for neodymium, samarium, gadolinium and terbium respectively. The magnetic structures of NdCoSi and TbCoSi consist of ferromagnetic (001) R layers (with moments lying in the plane) antiferromagnetically coupled along the c-axis with the sequence + + - - (at 2 K, mu = 2.08(4) mu(B) and 8.1(1)mu(B)) for Nd and Tb respectively). In all compounds, no local moment was detected on the cobalt site. The results are discussed and compared with those obtained on the closely related RCo2Si2, and isotypic RCoGe, RFeSi and RRuSi compounds.