Summary: A new formulation of Kapila’s five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The new formulation uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which exchange terms are derived from physical laws. All equations are written as a single system of equations in integral form. No equation is used to describe the topology of the two-fluid flow. Relations for the Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the exchange terms is proposed. The exchange terms have distinct contributions in the cell interior and at the cell faces. For the exchange-term evaluation at the cell faces, the same Riemann solver as used for the flux evaluation is exploited. Numerical results are presented for two-fluid shock-tube and shock-bubble-interaction problems, the former also for a two-fluid mixture case. All results show good resemblance with reference results.