Abstract: Hybrid stress elements and isoparametric elements are adopted to calculate stress intensity factors and J-integral of plane cracks in this paper. At every crack tip, an array of singular hybrid stress elements as sectors with parabolical arcs is arranged. Each sector is connected to a quadrilateral isoparametric element with eight Nodal points. The principle how to use the two types of elements mixedly is interpreted in this paper. The advantages of the method are the following.（ 1 ） The singular elements adopted as sectors can give a better description of the hoop stress distribution in the vicinity of a crack tip;（ 2 ） The isoparametric elements are adaptable to every kind of curve boundary, and simple and convenient to calculate;（ 3 ）J-integral can be calculated quite accurately in the isoparametric element region, so that it can be extended to elasto-plasticity calculation of plane cracks.Three numerical examples are given as follows:（ 1 ） a rectangular sheet with equal length edge cracks in both sides;（ 2 ） a rectangular sheet with a long crack in single side; （ 3 ） a rectangular sheet with a oblique crack.Every sheet is stressed under single uniform tensile load. 216-256 degrees of freedom are adopted in every example respectively. Comparison o f the obtained results with those of analytical and other singular element solutions shows that the values of the stress intensity factors obtained in every example, whether those were solved from the linear equations or came from J-integral values, are all in good agreement. The errors are only within 1 - 2 %. The scatter degrees of J-integrals from 4 - 6 integral pathes in each example are only within±0.7%.By carrying out practical calculations it is shown that the advantages of the method are high accuracy, reduced computer run time, and adaptability to practical application.