First principles electronic structure calculations reveal both SnP and SnSb to be stable in the NaCl structure. In SnSb, a first order phase transition from NaCl to CsCl type structure is observed at around 13 GPa, which is also confirmed from enthalpy calculations and agrees well with experimental and other theoretical reports. Calculations of the phonon spectra, and hence the electron-phonon coupling λep and superconducting transition temperature Tc, were performed at zero pressure for both the compounds, and at high pressure for SnSb. These calculations report Tc of 0.614 K and 3.083 K for SnP and SnSb respectively, in the NaCl structure-in good agreement with experiment-whilst at the transition pressure, in the CsCl structure, a drastically increased value of Tc around 9.18 K (9.74 K at 20 GPa) is found for SnSb, together with a dramatic increase in the electronic density of states at this pressure. The lowest energy acoustic phonon branches in each structure also demonstrate some softening effects, which are well addressed in this work. © 2017 IOP Publishing Ltd Printed in the UK.