Introduction: Partially controlled acute pain after abdominal surgery is associated with a variety of unwanted postoperative consequences, like respiratory complications, delirium, myocardial ischaemia, prolonged hospital stays, and chronic pain later on. A good postoperative recovery depends greatly on a proper analgesic regimen. While epidural analgesia has been used to provide postsurgical abdominal pain relief, peripheral nerve blockade is a good alternative. Aim: To compare the analgesic efficacy of Transverse Abdominis Plane (TAP) block and Epidural block in patients undergoing nephrectomy. Materials and Methods: In this single-blinded parallel-group randomised controlled study was conducted in the Department of Urology at the Institute f Postgraduate Medical Education and Research in Kolkata, West Bengal, India from November 2021 to October 2022. A total of 78 patients (18-65 years) with American Society of Anaesthesiologists (ASA) Grade-I and II were randomly assigned to Group-EA (Epidural) and Group-TA (TAP Block). Group-EA received 11 mL of 0.125% bupivacaine, and Group-TA received 11 ml of 0.125% bupivacaine, both given at an 8-hour interval for 24 hours. The primary outcome was to compare postoperative pain using the Visual Analogue Scale (VAS) score at 1, 8, 12, and 24 hours after surgery. Secondary outcome measures included assessing motor function using the Bromage Score, monitoring haemodynamic parameters (pulse rate, mean arterial pressure), and evaluating Postoperative Nausea and Vomiting (PONV). A p-value <0.05 was considered statistically significant when comparing the data. Results: The authors found that the distribution of male and female patients (p=0.650), ASA Grades (I:II) (p=0.515), mean age (p=0.899), and mean SpO2 (p=0.404) were comparable between the two groups (p>0.05). The pain scores between the EA and TA groups at 1, 8, 12, and 24 hours (0.10 vs. 0.08, 0.74 vs. 0.82, 1.00 vs. 1.31, 1.80 vs. 1.92) showed no significant difference at the specified times. However, the comparison of the mean Bromage scores in the EA and TA groups at the same time intervals (1 vs. 1.15, 1.08 vs. 2.51, 1.97 vs. 3.21, 1.97 vs. 4.74) revealed a significantly higher value in the TAP block group compared to the Epidural block group. The Epidural group had significantly lower blood pressure and pulse rate but experienced more PONV (15.4 vs. 2.6) compared to the TAP block group. Conclusion: Epidural block resulted in hypotension, bradycardia, shivering, and PONV as side-effects, which were negligible in the TAP block group. However, postoperative analgesia was quite comparable between the two groups. Postoperative pain, as assessed by VAS score, changed significantly in the TAP block group (intragroup p-value=0.0063), whereas it remained constant in the epidural group (intragroup p-value 0.094), and the difference between the two groups was statistically insignificant. The occurrence of hypotension, bradycardia, and PONV was significant in the epidural group, whereas postoperative mobility was better in the TAP group.