The　equation　describing　the　transport　process　of　contaminant　in　a　small-strain　deformation　soil　is　a　second-order　partial　differential　equation,　in　which　the　coefficients　are　variables.　By　now,　it　can　only　be　solved　by　numerical　method.　A　finite　difference　scheme　of　the　equation　was　derived　by　numerical　integration　method,　and　the　stability　of　the　scheme　was　proved　by　using　energy　method　for　the　established　initial-boundary　value　problem.　Finally,　the　finite　difference　scheme　was　used　to　simulate　the　transport　process　of　contaminant　in　rigid　soil,　and　numerical　solution　and　analytical　solution　were　compared.　Results　show　that　the　numerical　solution　is　consistent　with　the　analytical　solution,　implying　that　the　established　finite　difference　scheme　is　practical　when　it　is　stable.　Hence,　the　established　difference　scheme　can　be　used　to　solve　the　solute　transport　problem　in　a　small-strain　deformation　soil.