This study deals with the process and benefits of generating aerodynamic indicial admittance functions with the support of computational fluid dynamics based on the Euler equations. A simple parametric analytical approximation is alongside developed based on linear lifting line and piston theory, for the sake of assessing the physical consistency of numerical solutions while investigating the suitability of theoretical models in the subsonic regime. Thin elliptical wings are hence considered and the design space is described by three parameters: wing aspect ratio (6, 8, 12, 20), free stream Mach number (0.3, 0.5, 0.6) and flow perturbation type (angle of attack step, vertical sharp-edged gust). All numerical simulations exhibit good quality and weak sensitivity to parameters other than Mach number and flow aspect ratio, accounting for their combined effects. The benefit of using numerical results to tune analytical approximations and improve their accuracy is finally demonstrated by matching both initial and final behaviours of the wing lift development, with an effective synthesis of the high-fidelity features in the low-fidelity model.