We evaluated the effects of concurrent use of methotrexate and celecoxib on silent liver and kidney damages in rheumatoid arthritis (RA) patients. We enrolled 92 RA patients with normal laboratory results related to liver and kidney functions, who had received methotrexate and celecoxib concurrently over 6 months. Liver stiffness measurement (LSM) using transient elastography and ultrasonography were performed along with blood and urine tests. Estimated glomerular filtration rate (eGFR) was calculated by both the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and the Modification of Diet in Renal Disease (MDRD) equations. Initial eGFR represented kidney function at the time of the initiation of celecoxib. The cutoff for abnormal LSM values was adopted as 5.3 kPa. The optimal cutoff of each eGFR for abnormal LSM values was also calculated. The median age of patients was 55 years old (74 women). The median LSM was 4.4 kPa and the median eGFRs and median initial eGFRs ranged from 89 to 99 mL/min/1.73 m2. The cumulative doses of methotrexate and celecoxib and their concurrent administration duration did not affect LSM values and eGFRs. Both eGFRs were significantly associated with LSM values. Patients with initial eGFR(CKD-EPI), initial eGFR(MDRD), and eGFR(CKD-EPI) below each optimal cutoff had significantly high risks for silent liver fibrosis (RR 9.4, 10.3, and 4.4, p < 0.001, respectively). Both initial eGFRs (CKD-EPI and MDRD) and eGFR (CKD-EPI) were significant predictors for the development of silent liver fibrosis in RA patients who had received methotrexate and celecoxib concurrently for at least 6 months.