Micro-finite element models (μFEMs) are one of the critical components of the microscale analyses that are typically performed on trabecular bone. These models are often derived from on micro computed tomography (μCT) data and tend to encompass an extremely large number of elements that in turn require significant processing time and power. To address the increased computational demands, the main goal of the current study was to devise an algorithm capable to manage the large μCT data in order to construct Cartesian μFEMs. For this purpose, the developed technique relies on the projection of μCT voxels to a structured grid and were designed to involve fast integer operations and hashing techniques for fast mesh constructions. The numerical tests performed on common computer hardware revealed that only 55.16 seconds are required to discretize more than 36.2M voxels. Furthermore, the linear time complexity of the developed algorithm ensures that its efficiency will be preserved even in case of larger datasets that tend to be prevalent in micro-structural biomechanical analysis.