Modeling of unsaturated porous flow requires the knowledge of soil hydraulic functions. Such functions often involve multiple soil parameters that need to be estimated for different soil types. This study explores the use of a single-parameter hydraulic functions based on the linear-type K-η−ψ relationship applied in stochastic subsurface hydrology [1-3]. We first estimate the parameters of above linear-type K-η−ψ relationship through widely used soil hydraulic functions. Then we explore the possibilities and implications of expressing those parameters with a single soil parameter and few constants. Our results suggest that those constants are not very sensitive to the variation of soil parameters and a single-parameter soil hydraulic functions yield reasonably accurate representation. Preliminary validation of the proposed model using observed data yields promising results.