The mobility of Cd, Co, Cu, Ni, and Zn in podzols and organic soils (Histosols) in the area of long-term pollution from the Monchegorsk copper–nickel plant (Murmansk oblast, Russia) has been assessed using the parameters of diffusion and convection–diffusion models. The found values of diffusion parameters match the data for other regions. In most cases, the convective flow of heavy metals is directed downwards and has a velocity of 0.126 to 0.31 cm/yr, or it does not differ from zero in a statistically significant manner. On the average, podzols and organic soils are similar in the diffusion parameters with regard to the total heavy metal content but differ in the velocity of convective transfer, which is much slower in organic soils. The model estimates for the inflow of heavy metal pollutants to soil do not depend on the distance from the plant, although a correlation with soil type is observable: an additional lateral influx of heavy metals to the surface most likely takes place in organic soils, associated with local depressions. An insufficient sample volume does not permit to assess the correlation of migration parameters with soil properties, while their correlation with chemical mobility (extraction with ammonium acetate buffer) appears as an insignificant trend.