Stochastic approaches are useful to quantitatively describe transport behavior over large temporal and spatial scales while accounting for the influence of small-scale variabilities. Numerous solutions have been developed for unsaturated soil water flow based on the lognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochastic solutions for unsaturated flow have been derived on the basis of the normal distribution of hydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow by assuming the normal distribution of saturated hydraulic conductivity (Ks). Under the assumption that soil hydraulic properties are second-order stationary, analytical expressions for capillary tension head variance (σ2h) and effective hydraulic conductivity (K*ii) in stratified soils were derived using the perturbation method. The dependence of σ2h and K*ii on soil variability and mean flow variables (the mean capillary tension head and its temporal and spatial gradients) and mean flow conditions (wetting and drying) were systematically analyzed. The calculated variance of capillary tension head with the analytical solution derived in this paper was compared with field experimental data. The good agreement indicates that the analytical solution is applicable to evaluate the variance of capillary tension head of field soils with moderate variability.