Based on the structural characteristic of metal drill collar for induction logging while drilling, we have given the analytical formulae of lengthways fields Ez and Hz when the tool is located in a fan-ring shaped slot of drill collar by the boundary conditions of electromagnetic field, and derived the other components of electromagnetic field in and out the fan-ring slot from Ez and Hz. In the other intervals of formation, where the drill collar is a solid cylinder, the analytical formulae of field are educed through the method of variable coefficient. The total analytical solutions of field in whole space have been obtained. With the help of the analytical formulae, we have also given numerical examples and analyzed the distributive characteristic of electromagnetic field. From the computational results we find that the secondary scattering field Hz is in a linear relation with the conductivity of stratum. The characteristic of field is very useful for induction logging while drilling, which can be used to measure and analyze the logging responses of the stratum conductivity. This paper sets up a theoretical foundation for us to study the distrbutions of field and to direct the design of logging instruments. Based on the structural characteristic of metal drill collar for induction logging while drilling, we have given the analytical formula of of lengthways fields Ez and Hz when the tool is located in a fan-ring shaped slot of drill collar by the boundary conditions of electromagnetic field, and derived the other components of electromagnetic field in and out the fan-ring slot from Ez and Hz. In the other intervals of formation, where the drill collar is a solid cylinder, the analytical formula of the fields are educed through the method of variable coefficient . The total analytical solutions of field in whole space have been obtained. With the help of the analytical formulae, we have also given numerical examples and analyzed the distributive characteristic of electromagnetic field. From the computational results we find that the secondary scattering field Hz is in a linear relation with the conductivity of stratum. The characteristic of field is very useful for induction logging while drillin g, which can be used to measure and analyze the logging responses of the stratum conductivity. This paper sets up a theoretical foundation for us to study the distrbutions of field and to direct the design of logging instruments.