A fracture theory for concrete, a heterogeneous material with gradual strain-softening due to microcracking, is developed. The theory considers only Mode I cracks, modeled as blunt smeared crack bands, justified by the random microstructure. Simple triaxial stress-strain relations are derived to model strain-softening and microcracking effects. Compliance matrices are preferred over stiffness matrices, with only a single diagonal term adjusted. The fracture energy, uniaxial strength, and crack band width are the three material parameters, with the strain-softening modulus depending on them. A method to determine fracture energy from stress-strain data is provided. Triaxial effects are considered, and the theory is validated against experimental data, showing good agreement with load and resistance data. The optimal crack band width is about three aggregate sizes, justified for homogeneous modeling. Implementation in finite element codes is indicated, with rules for objective results. A formula predicts fracture energy and strain-softening modulus from tensile strength and aggregate size. Statistical analysis shows improved accuracy over linear fracture and strength theories. The theory is validated against experimental data, showing realistic results across all sizes, including the transition range. Deviations from linear fracture mechanics in concrete are due to its heterogeneity, causing a large nonlinear zone near the fracture front. This is similar to ductile fracture in metals but with a larger fracture process zone in concrete due to large aggregate sizes. The J-integral is inapplicable in strain-softening regions, and fracture energy is used instead. Concrete cracking is modeled as smeared cracks in finite elements, with fracture energy as the cracking criterion. The theory is developed based on a 1981 report and is applicable to Mode I cracks, which dominate in concrete.A fracture theory for concrete, a heterogeneous material with gradual strain-softening due to microcracking, is developed. The theory considers only Mode I cracks, modeled as blunt smeared crack bands, justified by the random microstructure. Simple triaxial stress-strain relations are derived to model strain-softening and microcracking effects. Compliance matrices are preferred over stiffness matrices, with only a single diagonal term adjusted. The fracture energy, uniaxial strength, and crack band width are the three material parameters, with the strain-softening modulus depending on them. A method to determine fracture energy from stress-strain data is provided. Triaxial effects are considered, and the theory is validated against experimental data, showing good agreement with load and resistance data. The optimal crack band width is about three aggregate sizes, justified for homogeneous modeling. Implementation in finite element codes is indicated, with rules for objective results. A formula predicts fracture energy and strain-softening modulus from tensile strength and aggregate size. Statistical analysis shows improved accuracy over linear fracture and strength theories. The theory is validated against experimental data, showing realistic results across all sizes, including the transition range. Deviations from linear fracture mechanics in concrete are due to its heterogeneity, causing a large nonlinear zone near the fracture front. This is similar to ductile fracture in metals but with a larger fracture process zone in concrete due to large aggregate sizes. The J-integral is inapplicable in strain-softening regions, and fracture energy is used instead. Concrete cracking is modeled as smeared cracks in finite elements, with fracture energy as the cracking criterion. The theory is developed based on a 1981 report and is applicable to Mode I cracks, which dominate in concrete.