The aim of the present paper is to provide a single analytical expression of the power transmission coefficient for leaky rays in multi-step index (MSI) fibres. This expression is valid for all tunnelling and refracting rays and allows us to evaluate numerically the power attenuation along an MSI fibre of an arbitrary number of layers. We validate our analysis by comparing the results obtained for limit cases of MSI fibres with those corresponding to step-index (SI) and graded-index (GI) fibres. We also make a similar comparison between this theoretical expression and the use of the WKB solutions of the scalar wave equation.