Axisymmetric centreline shock reflection takes place in a wide range of aerospace devices including intakes and nozzles of supersonic engines and space propulsion systems, representing significant implications to the performance and development of CubeSats/NanoSats, MEMS, micro-propulsion and hypersonic airbreathing propulsion technologies. When a conical shock impinges on an axis of symmetry, complex nonlinear wave interactions result in the formation of an irregular reflection structure, akin to Mach reflection in inviscid steady flow. Despite its widespread appearance, conical Mach reflection remains difficult to model on an analytical basis. In this paper, a new analytical method is proposed combining three-shock and curved shock theories to prescribe the shape of the incident shock and Mach disc. The results are compared to numerical flowfields from a Riemann solver and characteristics of conical shock reflection in the highly viscous regime are also examined.