Based on phase-field model，brittle fracture of the structures under tension is studied numerically. An introduction for construction of crack distribution function and energy dissipation function is presented. The governing equations for the phase field model are derived according to the conservation of energy and further solved by alternating minimization (staggered) algorithm. Good agreements between analytical solutions and numerical solutions of one-dimensional bar under tension validate the accuracy of analytical solutions. Numerical simulations of structures with geometric imperfection and predefined damage under tension are also presented. The numerical results show that deformation localization and brittle fracture in failure areas can be modeled accurately.