The article discusses the development of a kinetic solver for modeling pharmacokinetics. The architecture of an information-computing system was developed for the automated development of pharmacokinetics models based on a service-oriented paradigm, including: the sets of services necessary to create a system were determined, service interaction schemes for solving the problems of automated development of pharmacokinetics models within the framework of the system being developed are defined, necessary schemes and data exchange flows are defined, service interfaces have been developed. Implemented the ability to register new users of the system, create roles, grant rights. The data is studied using simplified models implemented by solver, the data is used at all stages of development, in particular for validation of the developed models, calculation of data on the sensitivity of the results to the model parameters. Algorithms of calculation based on pharmacokinetic models have been developed. Analytical solutions are found for solving systems of ordinary differential equations with initial conditions using pharmacokinetic models. Direct and inverse problems for linear one-two-three-chamber models of pharmacokinetics are solved. To check the results of calculating the models implemented in the Web Service, data testing was performed.