The two series of equiatomic rare earth (RE) stannides RENiSn and REPdSn were systematically studied with respect to high-pressure modifications. The normal-pressure (NP) low-temperature (LT) modifications were synthesized by arc-melting and subsequently treated under high-pressure (Pmax=11.5GPa) and high-temperature (Tmax=1570K) conditions in a Walker-type multi-anvil press. The pressure and temperature conditions were systematically varied in order to improve the crystallization conditions. The new ZrNiAl-type high-pressure modifications HP-RENiSn (RE=Sc, Y, La, Gd–Lu) and HP-REPdSn (RE=Y, Sm–Dy) were obtained in 80mg quantities, several of them in X-ray pure form. Some of the REPdSn stannides with the heavy rare earth elements show high-temperature (HT) modifications. The structures of HP-ScNiSn, HP-GdNiSn, HP-DyNiSn (both ZrNiAl-type), NP-YbNiSn, and HT-ErPdSn (both TiNiSi-type) were refined from single crystal diffractometer data, indicating full ordering of the transition metal and tin sites. TiNiSi-type NP-EuPdSn transforms to MgZn2-type HP-EuPdSn: P63/mmc, a=588.5(2), c=917.0(3) pm, wR2=0.0769, 211 F2 values, 11 variables. The structure refinement indicated statistical occupancy of the palladium and tin sites on the tetrahedral network. The X-ray pure high-pressure phases were studied with respect to their magnetic properties. HP-YPdSn is a Pauli paramagnet. The susceptibility data of HP-TbNiSn, HP-DyNiSn, HP-GdPdSn, and HP-TbPdSn show experimental magnetic moments close to the free ion values of RE3+ and antiferromagnetic ordering at low temperature with the highest Néel temperature of 15.8K for HP-TbPdSn. HP-SmPdSn shows the typical Van Vleck type behavior along with antiferromagnetic ordering at TN=5.1K. HP-EuPdSn shows divalent europium and antiferromagnetic ordering at 8.9K followed by a spin reorientation at 5.7K.