Adsorption　characteristics　play　a　crucial　role　in　solute　transport　processes,　serving　as　a　fundamental　factor　for　evaluating　the　performance　of　clay　liners.　Nonlinear　adsorption　isotherms　are　commonly　found　with　metal　ions　and　organic　compounds,　which　introduce　challenges　in　obtaining　analytical　solutions　for　solute　transport　models.　In　this　study,　analytical　solutions　are　proposed　for　a　fully　coupled　hydraulic-mechanical-chemical　(HMC)　model　that　accounts　for　both　the　Freundlich　and　Langmuir　isotherms.　To　mitigate　the　difficulties　arising　from　the　variable　coefficients,　the　system　of　second-order　partial　differential　equations　involving　three　variables　is　linearized.　The　method　of　separation　of　variables,　theory　of　integration,　and　Fourier　series　are　utilized　to　derive　analytical　solutions.　The　analytical　method　presented　can　potentially　be　extended　to　a　broad　spectrum　of　nonlinear　adsorption　isotherms.　The　results　reveal　a　56.5%　reduction　in　solute　breakthrough　time　under　the　Freundlich　isotherm　and　a　remarkable　2.6-fold　extension　under　the　Langmuir　isotherm　when　compared　to　the　linear　isotherm.　The　adsorption　constants　of　the　Freundlich　and　Langmuir　isotherms　exhibit　a　positive　correlation　with　breakthrough　time,　while　the　exponent　of　the　Freundlich　isotherm　and　the　maximal　adsorption　capacity　in　the　Langmuir　isotherm　demonstrate　a　negative　association　with　breakthrough　time.　This　study　enhances　the　precision　of　solute　transport　prediction　and　provides　a　more　scientific　assessment　of　clay　liner　performance.