The study focuses on analyzing stress concentration reduction around a single-side semicircular notch encased within a functionally graded material (FGM) layer. Notches, typical in structural elements, often exacerbate stress, which can lead to premature structural failure. In response, FGMs offer a potential solution by varying properties across their volume, thereby potentially mitigating stress concentration effects. The research explores the efficacy of three FGM types: Ni–Al2O3, Ti–TiB, and Al–SiC, under both tensile and bending loads. To conduct the analysis, the extended finite element method (XFEM) coupled with MATLAB is employed. This methodology enables a comprehensive investigation of stress concentration factors (SCFs) while varying FGM parameters. The results indicate a consistent trend: Al–SiC FGM consistently demonstrates superior stress distribution and exhibits the lowest SCF values compared to Ni–Al2O3 and Ti–TiB FGMs across different loading conditions. This consistency highlights Al–SiC as the optimal choice for stress concentration reduction around semicircular notches. A significant reduction in SCF is noticed, i.e., >40% in tensile load and > 50% in bending load condition. The findings underscore the critical role of FGMs in enhancing structural integrity and mitigating potential failure risks associated with stress concentration. By offering insights into the effectiveness of different FGM types, this research contributes valuable knowledge for the design and optimization of structures subjected to varying loading conditions.