Abstract <p>In this study, we analyze a piezomagnetic right-angle plane featuring a circular cavity and irregular boundaries utilizing the boundary element method. External loads in the form of SH waves and line sources acting on the piezomagnetic right-angle plane are taken into account. The efficacy of the boundary element method is demonstrated through two distinct illustrative scenarios. First, we assess the dynamic characteristics in the absence of line source loads on the irregular boundary, employing the image method and Graf addition theorem in the first scenario. Subsequently, we introduce Green’s identities and solve for the Green’s function in infinite three-dimensional space. In the second scenario, we explore the dynamic characteristics when irregular boundaries are subjected to line source loads using the boundary element method. Our findings elucidate the impact on the dynamic stress concentration factor and magnetic field intensity concentration factor under suitable conditions. Additionally, we compare analytical solutions with finite element solutions to corroborate the accuracy of the conclusions presented in this study.</p>