Despite the immense importance of micro, small and medium enterprises (MSMEs) to job creation and the alleviation of abject poverty, significant numbers of MSMEs cannot realize their full potential because of limited access to finance and other factors, mostly in developing countries. The study investigates micro, small and medium enterprises' access to finance constraints in Ethiopia from a demand-side perspective. This study employed a descriptive analysis using survey data collected from 814 randomly selected sample enterprises. The results show that about 76% of the MSMEs were established by initial capital majorly generated from their own savings, family or friends, Equub, and saving and credit cooperatives among others. The remaining 24% accessed their initial capital from formal financial institutions. From the total, 39.4% of MSMEs did not apply for loans due to high collateral requirements, complex application procedures, unfavorable interest rates, insufficient loan size, maturity, and grace period, and lack of transparency. The study results also reveal that 22%, 46%, and 32% of the MSMEs are partially credit constrained, fully credit constrained, and non-credit constrained, respectively. The difference between the average demand and the loan supplied is estimated to be 3241, 11444, and 30949 USD for each micro, small, and medium-sized enterprise, respectively. The total estimated finance gap for all MSMEs is 31.7 billion USD. The findings of this study suggest the establishment of public credit guarantee schemes, cash flow-based lending, and psychometric testing for credit scoring and automating the MFIs' services to improve MSMEs' access to finance.