Chronic renal failure or Chronic Kidney disease (CKD) is a condition threatened by many potential losses and changes in lifestyle. As the disease progresses, such patients physically may not be able to cope up and as such use various strategies to deal with the challenges related to their disease and the associated treatment procedures. The objectives of this study were i) to study the sociodemographic characteristics of the respondents ii) to assess the levels of stress and the coping strategies used by CKD patients who were on maintenance Hemodialysis and ii) study the relationship between stress and coping and their background characteristics. The sample consisted of 50 CKD patients who were on maintenance dialysis in Nephrology ward, Sri Venkateswara Institute of Medical Sciences, Tirupati. Measures such as Perceived Stress Scale (Sheldon Cohen, 1983) and Brief Cope (Carver, 1997s) were used to know the levels of stress and coping among the participants. The study results revealed a statistically significant relationship (at 0.05) level) between patients occupation, income and Stress. The results also revealed a significant relationship (at 0.000 level) between patients Coping styles and their living arrangements, and an overall significant relationship was found between Stress and Coping at 0.05 level. The present study concludes with the need for preparing patients for effectively coping with their disease condition and implications for social work intervention are also mentioned.