Unmanned Aerial Vehicles (UAV) have received an increasing amount of attention recently with many applications being actively investigated across the globe, and several related open research questions being actively pursued. Possible applications include search and rescue, disaster relief, environmental monitoring and surveillance, transportation, and construction. Transportation of cable suspended payloads using Unmanned Aerial Vehicles is one such application which is the topic of this research. Autonomous transportation of objects using UAV can contribute to the safe and reliable supply of food and medicine in remote or disaster-affected areas and even in commercial delivery of goods. The state-of-the-art approaches towards the slung load transportation either develop non-linear feedback control laws to stabilize the system to a predefined trajectory or employ open loop off-line trajectory planning schemes to generate optimal control inputs to the system. Most of these techniques often rely on availability of an accurate model of the system backed up with simulation results. Very few results exist which target experimental validation of the proposed method. Based on the findings of the previously conducted literature survey, it appears that the application of closed loop on-line trajectory generation and control schemes to transport a slung payload in swing free manner remains unanswered. The work in this thesis sets off to answer the research questions in this direction and address the issues that come along with experimental validation. Model Predictive Control (MPC) is a promising framework, which provides the means to tackle both the trajectory generation problem and the feedback control problem in an unified manner. As a result, it forms the most important component of this thesis. Specific research problem that is addressed in this thesis is to transport a cable suspended load using quadrotor from one point to another, while minimizing the swing through the use of Linear Time Invariant MPC techniques. A non-linear dynamic model for the quadrotor-slung load system is obtained and the structure within the system dynamics is exploited to decide the control strategy. Two different MPC formulations viz. MPC with integral action and MPC with delta-u formulation are simulated and compared to Linear Quadratic control with integral action which acts as a benchmark controller. Backed with simulation results, it is shown through experimental validation that it is possible to control the swing of cable suspended load using linear control techniques. MPC being an computationally expensive task, state-of-the-art fast optimization solvers such as FORCES PRO is used to achieve on-line implementation of MPC for the quadrotor-slung load system. To this end, a new software framework for implementation of MPC is developed which establishes a wireless link with the quadrotor resulting in a real-time networked control loop.