The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearence after the treatment with monoclonal antibodies (moAb). Here we present a mathematical model for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. To evaluate the drug performance we have developed equations for two types of tumors cells, i.e KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It was observed that even the minimal initial concentration of KRAS mutation before the treatment has the ability to make the tumor refractory to the treatment. Minor population of KRAS mutations has strong influence on large number of wild-type cells as well rendering them resistant to chemotherapy. Patient's immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them.