The (K, pi ) Sigma -hypernuclear spectrum is studied, using a simple interaction model with a square-well central part and a delta function spin-orbit Sigma -nuclear core interaction. With this simplified model the general features of the spectrum are explained. A comparison is made between the theoretical results and the in-flight (K, pi ⁺) experimental data for _Sigma¹²C and _Sigma¹⁶O. A shallow potential, with a central potential depth of V_c=(-5-115) MeV and a spin-orbit depth of V_so=15 MeV, gives a satisfactory representation of the CERN and BNL in-flight data.