Using the approach developed earlier for the description of the electron-photon showers in axially aligned single crystals, some characteristics of the positron yield measured in recent experiments are calculated. Theoretical estimations display a rather good agreement with experimental results obtained using 3 to 10 GeV electrons aligned to the axis of the tungsten crystals. Such comparison verified that the accuracy of our approach is quite sufficient to make a reliable choice for optimal parameters of the positron source using axially aligned crystals for future linear colliders.