This paper presents the application of a mathematical model for simulation of the swirling flow in a tube induced by elliptic-cut and classical twist tape inserts. Effects of the twist ratio (y=2.93, 3.91, and 4.89) and cut depth (w=0.4, 0.8, and 1.4 cm) on heat transfer enhancement (Nu) and friction factor (f) in laminar flow are numerically investigated. The simulation is carried out using commercial CFD package (FLUENT-6.3.26) to grasp the physical behaviour of the thermal and fluid flows of a constant heat-fluxed tube fitted with elliptic-cut twist tape in the laminar flow regime for the Reynolds number ranging from 200 to 2100. The simulated results matched the literature correlations of plain tube for validation with 8% variation for Nusselt number and 10% for friction factor. The results show that the heat transfer rate and friction factor in the tube equipped with elliptic-cut twist tape (ECT) are significantly higher than those fitted with classical twist tape (CTT). Moreover the results also reveal that the Nusselt number and the friction factor in the tube with elliptic-cut twisted tape (ECT) increase with decreasing twist ratios (y) and cut depths (w).