Stone wool materials have gained considerable attention due to their effectiveness as thermal and acoustic insulation solutions. The comprehension of crystal structure properties is pivotal in determining the overall performance of these materials, as it enables us to optimize their composition for enhanced insulating capabilities. Crucial factors such as structural, mechanical, and thermodynamic characteristics of crystalline phases within stone wool are vital for evaluating its thermal and acoustic insulation properties. This study investigates the properties of calcium aluminum silicate crystal phases commonly present in stone wool, including anorthite, svyatoslavite, scolecite, and dehydrated scolecite using density functional theory (DFT) calculations. In comparison to previous works, this study provides a more comprehensive analysis using advanced DFT calculations. Our analysis reveals the complex interplay between the crystal structures and mechanical behavior of these phases. The calculated bulk modulus of the phases varies significantly, ranging from 38 to 83 GPa. We have compared the calculated elastic properties with available experimental data and found excellent agreement, confirming the accuracy of the computational approach. Moreover, we find that polymorphism has a significant impact on the mechanical strength, with anorthite exhibiting higher strength compared to svyatoslavite. Furthermore, dehydration is found to cause a reduction in unit volume and mechanical strength. The thermodynamic properties of dehydrated scolecite, including entropy and heat capacity, are significantly lower due to the absence of water molecules. These findings highlight the importance of understanding the structural and mechanical characteristics of calcium aluminum silicate phases in stone wool materials. Additionally, our findings have broader implications in various industries requiring effective insulation solutions such as to develop new materials or to enhance the energy efficiency of existing insulating products.