Primary HID kinetic isotope effects for the [1,5] hydrogen shift reaction in 13-atomic 1,3-pentadiene and [1,7] hydrogen shift reaction in 23-atomic 7-methylocta-1,3,5-triene are calculated using the semiclassical instanton approach. All 33 and 63 internal degrees of freedom, respectively, are treated quantum mechanically with multidimensional tunneling automatically accounted for by the instanton approach. Reactive potential energy surfaces are calculated on-the-fly using mPW1K/6-31+G(d,p) and mPWB1K/6-31+G(d,p) electronic structure methods. The calculated kinetic isotope effects agree well with the previously reported experimental measurements. The analytical expressions of the semiclassical instanton approach allow one to determine quantitative contributions of various physical mechanisms to the calculated kinetic isotope effects. Multidimensional tunneling is found to play important role in both studied hydrogen shift reactions.