Cold atmospheric plasmas have attracted significant worldwide attention for their potential beneficial effects in cancer therapy. In order to further improve the effectiveness of plasma in cancer therapy, it is important to understand the generation and transport of plasma reactive species into tissue fluids, tissues and cells, and moreover the rates and depths of delivery, particularly across physical barriers such as skin. In this study, helium (He) plasma jet treatment of a 3D cancer tumour, grown on the back of a live mouse, induced apoptosis within the tumour to a depth of 2.8 mm. The He plasma jet was shown to deliver reactive oxygen species through the unbroken skin barrier before penetrating through the entire depth of the tumour. The depth and rate of transport of He plasma jet generated H₂O₂, NO₃ ^- and NO₂ ^-, as well as aqueous oxygen [O₂(aq)], was then tracked in an agarose tissue model. This provided an approximation of the H₂O₂, NO₃ ^-, NO₂ ^- and O₂(aq) concentrations that might have been generated during the He plasma jet treatment of the 3D tumour. It is proposed that the He plasma jet can induce apoptosis within a tumour by the 'deep' delivery of H₂O₂, NO₃ ^- and NO₂ ^- coupled with O₂(aq); the latter raising oxygen tension in hypoxic tissue.