A stepped capillary tube is a new design that consist of two serial connected capillary tubes with different diameter as an alternative in order to reduce the manufacturing cost of the typical assembly of two capillary tubes and a by-pass check valve widely used to achieve different mass flow rates in residential heat pump systems. One-dimensional numerical modelling of fluid-flow inside stepped capillary tubes was performed, and successfully validated against experimental data. Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-bystep method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement were also considered. These results demonstrate a robust application of the model developed to predict reliably the mass flow rate through stepped capillary tubes, which enable this tool to be reliably used for the design of this kind of systems.