Driven by the explosive growth of Internet of Things (IoT) devices with stringent requirements on latency and reliability, ultra-reliability and low latency communication (uRLLC) has become one of the three key communication scenarios for the fifth generation (5G) and beyond 5G communication systems. In this paper, we focus on the beamforming design problem for the downlink multiuser uRLLC systems. Since the strict demand on the reliability and latency, in general, short packet transmission is a favorable form for uRLLC systems, which indicates the literature Shannon's capacity formula is no longer applicable. With the finite blocklength transmission, the achievable delivery rate is greatly influenced by the reliability and latency. Using the developed achievable delivery rate formula for finite blocklength transmission, we respectively formulate the problems of interest as the weighted sum rate maximization, energy efficiency maximization, and user fairness optimization by considering the maximum allowable transmission power and minimum rate requirement. It's worthy pointing out that this is the first work to design the beamforming vectors for the downlink multiuser uRLLC systems. To address these non-convex problems, some important insights have been discovered by analyzing the function of achievable delivery rate. For example, the minimum rate requirement can be realized by low bounded the signal-to-interference-plus-noise ratio. Based on the discovered results, we provide algorithms to optimize the beamforming vectors and power allocation, which are guaranteed to converge to a local optimum solution of the formulated problems with low computational complexity. Our simulation results reveal that our proposed beamforming algorithms outperform the zero-forcing beamforming algorithm with equal power allocation widely used in the existing literatures.