The previous concept of non-uniform stagnant motions (NUSM) is applied to the analysis of steady and transient extensional flow realized in certain types of rheometers, including, in particular, the spin-line rheometer (SLR), the filament stretching rheometer (FSR) and the rotary clamp extensometer (RCE). It is shown that the corresponding approximate solutions depend on two material functions as well as on the specimen geometry. It also turns out that the transient extensional viscosity function and extensional modulus determined on the basis of quasi-elongational approximations may be overestimated or underestimated as compared with more realistic values resulting from the present considerations.