In the estimation of strength of metals, it is of great importance to clarify the singular behavior of stresses and strains at tips of cracks. As we know, monocrystalline metals are mostly anisotropic. Plastic anisotropy in polycrystalline metals arises from preferred crystallographic orientation of grain and/or the development of texture due to prior plastic deformation. composite materials may be treated as macroscopically homogeneous, but anisotropic if the characteristic size of fiber, such as the fiber diameter as well as fiber spacing, is small compared with the relevant macroscopic dimension of the composite system e.g. the plastic zone size, physical dimension of the components,and other characteristic macroscopic lengths.Since tips of cracks are always accompanied by plastic zones when failure takes place, it is expected that plastic properties, such as work-harding and plastic anisotropy, play important roles in the failure of metals. As a consequence, it is highly necessary to study the effect of work-harding and plastic anisotropy on the singular stress and strain fields at the tip of a crack.In this paper, in view of a phenomenological plasticity theory for orthotropic material proposed by Hill, some problems about near-tip fields in orthotropic materials are discussed in detail. The following solutions at near-tip fields are obtained for the first time.(i) Asymptotic fields at the tips of the Mode III stationary crack and steady dynamic crack growth in elastoplastic materials with plastic orthotropy:(ii) Asymptotic fields at the tips of the Mode III stationary crack and steady dynamic crack growth in power-law harding orthotropic materials.(iii) The near-tip fielfs for plane stress Mode I stationary crack in elastoplastic materials with plastic orthotropy.(iv) Plane strain asymptotic fields of Mode I steady dynamic crack growth in power-law harding orthotropic medium.The asymptotic solution of plane strain mixed mode stationary crack problem in an elastoplastic material with plastic orthotropy is reconsidered. There are no discontinuous lines in stess field, which is different from J. Pan’s results.It is shown that the field solution is not unique for problems of plane stress or plane strain stationary crack in an elastoplastic medium with plastic orthotropy. There are free parameters in the stress firlds. The far field conditions are needed for the determination of the solutions.It is found that the order of singularity of the stresses in the vicinity of the stationary crack tip is the same as that in the case of isotropic materials, but the amplitudes are greatly influenced by the orthotropy. The orthotropy in the problems of steady dynamic crack growth influences singularity of stress and strain and exist condition of elastic unloading zone, which is different from that in the case of isotropic materials. Through numerical calculation for some typical crack-tip fields, we can see the effect of the material’s orthotropy. Resonable fracture criteria can be established according to these reliable theoretical results.The method in this paper can be used to predict singular behavior of monocrystalline metals. It is valuable for the study of fracture problems in composite materials.