A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry - relies on the ability to compute resonance spectra accurately and efficiently. Established methods for calculating these spectra are either fast but limited to simple geometries, or are applicable to arbitrarily shaped samples at the cost of being prohibitively slow. Here, we describe a method to rapidly compute the normal modes of irregularly shaped objects using entirely open-source software. Our method's accuracy compares favorably with existing methods for simple geometries and shows a significant improvement in speed over existing methods for irregular geometries. © 2023 Acoustical Society of America.