[en] A capillary modification of the method of measuring trace elements and radionuclides diffusivity in soils, clays and bentonites is described. The method is based on the diffusion from an infinitely thin labelled layer (paper disc) through a very thick layer of the moist material in a glass capillary hermetically closed at both sides, on the consecutive sectioning of thin layers of the material pressed out of the capillary after the diffusion, and on measuring their specific activities. The effective diffusion coefficient D_ef (for ¹³⁷Cs, ⁸⁵Sr, ⁶⁵Zn) was calculated by using the solution of Fick's 2nd law. The dependences of D_ef on moisture, distribution coefficients K_d of the given nuclides, size of the material particles, and pH of medium were examined. The findings of the diffusivity studied are as follows: validity of Fick's laws in the given media; increasing D_ef and K_d with increasing moisture; for soil samples with particle dimensions < 0.047 cm the values of D_ef(¹³⁷Cs) are by one order of the magnitude lower than for samples with particle dimensions < 0.08 cm; sorption of ¹³⁷Cs is substantially greater than for ⁸⁵Sr and D_ef(⁸⁵Sr) was several times greater than D_ef(¹³⁷Cs); D_ef(¹³⁷Cs) < D_ef(⁶⁵Zn) < D_ef(⁸⁵Sr) which corresponded with K_d values, i.e. K_d(¹³⁷Cs) is 10 times greater than K_d(⁶⁵Zn) and K_d(⁸⁵Sr), which are of the same order. Of importance was the comparison of diffusivity data at near moistures in soil and clay: D_ef values in clay are by one order of magnitude lower than in soil. The possible influence of the prediffusion rest time prior to the diffusion on establishing physico-chemical equilibrium in the material hermetically closed in the capillary was also studied. The study also concentrated on the influence of shaking time in the closed vessel