- We consider string meson and string baryon models in the framework of the modified measure theory, the theory that does not use the determinant of the metric to construct the invariant volume element. As the outcome of this theory, the string tension is not placed ad hoc but is derived. When the charges are presented, the tension undergoes alterations. In the string meson model there are one string and two opposite charges at the endpoints. In the string baryon model there are two strings, two pairs of opposite charges at the endpoints and one additional charge at the intersection point, the point where these two strings are connected. The application of the modified measure theory is justified because the Neumann boundary conditions are obtained dynamically at every point where the charge is located and Dirichlet boundary conditions arise naturally at the intersection point. In particular, the Neumann boundary conditions that are obtained at the intersection point differ from that considered before by 't Hooft in [hep-th/0408148] and are stronger, which appears to solve the nonlocality problem that was encountered in the standard measure approach. The solutions of the equations of motion are presented. Assuming that each endpoint is the dynamical massless particle, the Regge trajectory with the slope parameter that depends on three different tensions is obtained.