Summary: Developing a numerical method to accurately simulate the brittle crack propagation phenomenon is crucial for ensuring the safety of large-scale steel structures. Although recent studies have demonstrated that using the local fracture stress criterion as the fracture condition is effective, the most critical issue is that the methods for evaluating local stress in the vicinity of the dynamically propagating crack front have not been established. To address this, this paper proposes a strategy for analysing a dynamically propagating crack in 3D solids on the basis of the s-version finite element method (s-method). In the proposed strategy, the local mesh is defined in the vicinity of the crack front as an ideal structured mesh aligned with both the crack front direction and crack propagation direction to accurately simulate the local stress field. The dynamically propagating crack front was modelled by a combination of the nodal force release method and local mesh update. The proposed strategy was verified by evaluating the accuracies of the local stress in stationary and dynamically propagating circular crack problems as well as those of the stress intensity factor. The results demonstrate that the proposed strategy provides unprecedented accuracy and efficiency of local stress evaluation in problems of dynamic crack propagation in a 3D solid without requiring any complicated remeshing procedures. Therefore, the proposed strategy has potential as the basis of a numeral framework for analysing dynamic brittle crack propagation problems dominated by the local fracture stress criterion.