The deformation of the solid matrix affects the fluid pore pressure and flow by altering the pore volume. Such interaction in turn affects the storage of groundwater in the void space. Obviously, this subject is of interest in groundwater hydrology. This paper describes an investigation of the effect of aquifer heterogeneity on the variability of the fluid pressure head and solid's volume strain, where the assumption of a constant vertical total stress leads to a relatively simple relationship between changes in solid's volume strain and fluid pressure head. To solve the problem analytically, focus is placed on the one-dimensional models. It is found from our closed-form solutions that the variance and correlation length of the log hydraulic conductivity are important in increasing the variability of pressure head and solid's volume strain. It is hoped that our findings will provide a basic framework for understanding and quantifying field-scale volume strain processes and be useful in stimulating further research in this area.