Exciton spectra of monolayer transition metal dichalcogenides (TMDs) in various dielectric environments are studied using an effective mass model incorporating a screened two-dimensional (2D) electron-hole interaction described by the Keldysh potential. Exciton states are calculated by solving a radial equation (RE) with a shooting method including Runge-Kutta integration. Particular attention is paid to the simple models for 2D exciton calculation. The 2D hydrogen model yields much lower exciton energies than the Rydberg series from the RE solution. The screened hydrogen model (SHM) [Phys. Rev. Lett. 116, 056401 (2016)] is examined by comparing its exciton spectra with the RE solutions. While the SHM is found to describe the nonhydrogenic exciton Rydberg series (i.e., the energy's dependence on main quantum number n) reasonably well, it fails to account for the linear decrease of the exciton energy with the orbital quantum number m. The exciton Bohr orbit shrinks as |m| becomes larger resulting in increased strength of the electron-hole interaction and a decrease of the exciton energy. The exciton effective radius expression of the SHM can characterize the exciton radius's dependence on n, but it cannot properly describe the exciton radius's dependence on m, which is the cause of the SHM's poor description of the exciton energy's m-dependence. For monolayer WS 2 on the SiO 2 substrate, our calculated s exciton Rydberg series agrees closely with that measured by optical reflection spectroscopy [Phys. Rev. Lett. 113, 076802 (2014)], while the calculated p excitons offer an explanation for the two broad features of a two-photon absorption spectrum [Nature 513, 214 (2014)]. Our calculated exciton energies for monolayer TMDs in various dielectric environments compare favourably with experimental data. Variational wave functions are obtained for a number of strongly bound exciton states and further used to study the Stark effects in 2D TMDs, an analytical expression being deduced which yields a redshift of the ground state energy to a good accuracy. The numerical solution of the RE combined with the variational method provides a simple and effective approach for the study of 2D excitons in monolayer TMDs. * Electronic address: phyjzzhang@jlu.edu.cn 2