Abstract Transition metal carbides and nitrides (MXenes) are considered the new generation of flexible electronic materials because of their superior mechanical strength and flexibility. Based on the density functional theory, the structures, electronic properties and mechanical properties of the 2D Zr-based MXenes with and without surface functional groups (O, F and OH) are investigated systematically to explore their elastic properties and tensile fracture mechanism. The results reveal the tensile strength and critical strain under biaxial tensile direction can reach 52 GPa, 12% for Zr₂C and 55 GPa, 19% for Zr₃C₂, more outstanding than the mechanical behavior of the pristine Ti₂C (47 GPa, 9.5%). The tensile behaviors of the functionalized Zr _{n +1}C_nT₂ (n = 1, 2, T = O, F, OH) strongly depend on the crystallographic orientation and the surface functional group. The phonon spectrum under the critical strain indicates the tensile fracture of the pristine Zr-based MXenes was determined by phonon instability, except along the armchair direction of Zr₂C and zigzag direction of Zr₃C₂. During tensile strain, the collapse of Zr _{n +1}C _n F₂ and Zr _{n +1}C _n (OH)₂ (n = 1, 2) are mainly caused by internal Zr–C bond rupture and transfer to the surface. While the O-functionalized Zr _{n +1}C _n O₂ (n = 1, 2) presented the opposite collapse trend. Additionally, according to the research results of critical strain, elastic modulus and electrical conductivity, F/OH-terminated Zr₂C MXene is relatively more suitable for flexible sensors of wearable devices than Zr₃C₂T₂.