This paper presents the design and simulation of acoustic metamaterial lenses that focus elastic waves at pre-determined focal points. The modified Luneburg refractive index profile is used in the design process to de-fine the focal point locations, which is a capability not previously explored in elastic wave research. This new approach is important because it enables more precise spatial control of waves, resulting in enhanced resolution for elastic wave focusing applications. Three lenses, each targeting specific focal points, are designed by pro-posing hexagonal unit cells containing blind holes with varying diameters. Dispersion curves are calculated by finite element simulations to determine wave properties of unit cells, including refractive indices. These unit cells provide a wide range of refractive indices (1.0314-1.4959) at the design frequency of 50 kHz which is suitable for constructing Luneburg lenses. Unit cells are then arranged according the discretized refractive index profiles to form the lenses. Numerical simulations validate effective wave focusing at the intended focal points (F=R, 1.5R, 2R) with three lenses. The highest amplification of waves and narrowest focal zone is for the lens with F=R. As focal point shifts toward 2R, wave distribution becomes scattered along the focal axis. Decay length analysis of F=1.5R and 2R lenses indicates their suitability for long distribution of high-velocity regions. Frequency-dependent simulations across 46–52 kHz reveal all lenses maintain efficient focusing be-tween 49–51 kHz. At more distant off-design frequencies, amplifications result from refractive index shifts that misalign the focal point.