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Unmanned Aerial Vehicles (UAVs) have been used on construction job sites for a variety of purposes for more than a decade. But the risks and hazards of flying UAVs on construction job sites has never been quantitatively or qualitatively evaluated. While the general aviation industry has been using sophisticated analysis techniques to quantitatively assess the risks of general aviation industry flights over the general population for decades, the risks of UAV flights over this group has never been quantitatively assessed. UAVs are being used in construction activities on a regularly without proper risk assessment. There is no action plan in place, by either construction managers or safety officers, to design UAV flights based on safety measures. This paper presents the first known quantitative and qualitative analyses of UAV flight risks for construction job sites. A quantitative model for UAV flight risk assessment is presented and tested, using the Monte Carlo simulation technique, for an actual construction job site. A qualitative risk assessment of UAV flights is also presented by combining the Federal Aviation Administration (FAA) rules, regulations and guidelines concerning UAV flights, with the safety needs and specifications of UAV flights on a construction job site. The techniques introduced in this paper can be used by construction managers and safety officers to take safety into account when planning UAV flights over construction job sites. This paper further argues that using techniques and methods introduced in this research paper could potentially make UAV flights in any environment safer and more reliable.