Lead and copper are heavy metals that are applied in different industries. Their standard limits in drinking water are 0.05 and 1.3 mg/L, respectively. Since natural absorbents are inexpensive and may be achieved without any cost and they are usually found in abundance in nature, absorption of solute ions by these materials is a proper method for eliminating heavy metals from polluted waters and industrial wastewaters. In this study, tea leaves and wheat straw wastes were used to absorb lead while sawdust and rice hull were applied to absorb copper from a polluted solution under batch and continuous conditions. The experiments have been carried out at different concentrations and times with an optimum pH of 5 and 5.5 for lead and copper, respectively. According to the batch experimental results, the equilibrium time has been found to be within the range of two hours. By increasing the concentration of absorbed material, the absorption efficiency has been diminished. The results of the batch experiments coincided with Langmuir and Freundlich isotherms but did not agree with BET and Linear isotherms. Continuous experiments have been accomplished with the use of an absorption column and a high up-flow rate of 0.35 L/min. In general, absorption efficiency has a decreasing trend over time. Based on the results of the continuous column system, the percentage maximum sorption of lead for tea leaves and wheat straw wastes came to be 99.5. This value for copper by sawdust and rice husk was found to be 95 and 63 percent, respectively.