Cloud computing offers storage, infrastructure, computing, networking, databases, platform, software, and analytics services over the Internet. It provides numerous benefits including scalability, cost management, broad access to resources, elasticity, resource pooling. Though cloud computing is mature and widely adopted computing model in software as well as non-software industries, it has several issues regarding security as it provides most of the cloud services over the public infrastructure. Denial of service (DOS), malware injection, insecure APIs, data loss, data breaches, hypervisor vulnerabilities, VM escape are a few major issues in cloud computing. In this paper, authors tried to provide a comprehensive analysis of critical security issues in cloud computing. Furthermore, this paper critically analyses the existing solutions to the various security issues in the cloud computing model.