The use of inhalational anaesthesia is ubiquitous in terrestrial vertebrates. Given the dependence of these agents on delivery by the cardiorespiratory system, we developed a new computational model predicting equilibration of inhaled anaesthetics in mammalian and ectotherm conditions including the ability of reptiles to maintain vascular shunts. A multi-compartment model was constructed from simultaneously-solved equations, verified by comparison to the literature for endo and ectotherm physiology. The time to 90% equilibration of anaesthetic in arterial blood (t₉₀) is predicted and used to compare anaesthetics and physiologies. The five to tenfold lower cardiac output and minute ventilation of ectothermic vertebrates is predicted to slow equilibration times by five to ten times leading to 90% equilibration in ectotherm arterial blood of over 200 min, compounded by reduction in body temperature, and the extent of right-to-left vascular shunts. The impact of these findings is also influenced by the solubility coefficient of the anaesthetic, such that at net right-to-left shunt fractions of over 0.8, sevoflurane loses the advantage of faster equilibration, in comparison with isoflurane. We explore clinical strategies to regulate anaesthetic uptake in ectotherms by managing convectional flow especially by supportive ventilation and reduction of the right-to-left shunt.