From the pure extension of the straight bar it can be seen that the balancing stress in the tilted section of the element can only ensure the balance of itself, but can’t ensure the balance of particles on it. The difference between the balance of the element and that of particles on it is demonstrated. A conclusion is drawn that the balancing stress of particles under two dimension stress state is written as σ＇_α = σ^2_x +σ²_y+ 2τ²+2τ（σ²_x+σ²_y）^1/2(sinα₂ + cosα₂))^1/2，and the angle between the direction of the balance stress and axis is written as α_x= arctan ( τ + (σ²_x + σ²_y)^1/2 sin arctan （σ_y/σ_x)) /（τ + （σ²_x+σ²_y）^1/2 cos arctan (σ_y/σ_x)). Under two dimension stress state, the principal stress of element and the maximum balancing stress of particles both take place in the 45°diagonal plane, and the balancing stress of particles is 2^1/2 times that of the principal stress. A new two dimension combining strength condition is derived as σ＇_α = (σ² + 2τ² + 2στ )^1/2≤[σ], and it will replace the formula of bend-torsion combining strength condition of third strength theory ( σ² + 4τ²)^1/2≤[σ] and that of fourth strength theory( σ² + 3τ²)^1/2≤[σ]. A new three dimension combining strength condition is derived as σ＇_d =(σ²₁+σ²₂+σ²₃)^1/2[σ]and can replace the wrong formula σ_xd=[((σ₁ -σ₂)² +(σ₂-σ₃)² +(σ₃-σ₁)²)/2 ]^1/2≤[σ] , which is the corresponding strength formula of the fourth strength theory.