Changes to building codes that enable use of materials such as cross-laminated timber (CLT) in mid- and high-rise construction are facilitating sustainable urban development in various parts of the world. Keys to this are the transition to multi-performance-based design approaches along with fewer limitations on heights or the number of storeys in superstructures constructed from combustible materials. Architects and engineers have increased freedom to apply new design and construction concepts and methods, as well as to combine timber with other structural materials. They also have started to develop wall arrangements that optimise interior space layouts and take advantage of the unique characteristics of CLT. This paper discusses the seismic response of multi-story buildings braced with a CLT core and perimeter shear walls anchored to foundations and floor platforms using modern high-capacity angle brackets and hold-downs, or X-Rad connectors. Linear dynamic finite element (FE) models of seismic responses of superstructures of various heights are presented, based on experimentally determined characteristics of wall anchor connections. Particular attention is given to fundamental vibration periods, base shear and uplift forces on walls, as well as inter-story drift. Discussion of FE model results focuses on structural engineering implications and advantages of using CLT to create shear walls, with emphasis on how choice of wall anchoring connections impacts the possible number of storeys and configurations of superstructures. Employing CLT shear walls with X-Rad or other types of high capacity anchoring connections makes possible the creation of building superstructures having eight and potentially more storeys even in high seismicity regions. However, it is important to emphasise that proper selection of suitable arrangements of shear walls for CLT buildings depends on accurate representation of the semi-rigid behaviors of anchoring connections. The linear dynamic analyses presented here demonstrates the need during engineering seismic design practices to avoid use of FE or other design models which do not explicitly incorporate connection flexibilities while estimating parameters like fundamental periods, base shear and uplift forces, as well as inter-story drift.