Numerical and experimental investigations are performed for the molecular transition and slip flows in pumping channels of a helical-type drag pump (HTDP) and disk-type drag pump (DTDP). The flow occuring in the pumping channel develops from the molecular transition to slip flow traveling downstream. Two different numerical methods are used in this analysis: the first one is a continuum approach in solving the Navier-Stokes equations with slip boundary conditions, and the second one is a stochastic particle approach through the use of the direct-simulation Monte Carlo method. From the present study of a HTDP, the numerical results of predicting the performance, obtained by both methods, agree well with the experimental data for the range of Knudsen number Kn less than or equal to 0.01 (i.e., the slip-how regime). But the results from the second method only agree with the experimental data for Kn>0.01 (i.e., the molecular-transition regime). From the analysis for a DTDP, we found that an actual pumping passage is strictly limited to a narrow region because of the significant backstreaming of molecules from the outlet.