Laser ultrasonic waves are promising tools for non-destructive inspection in various industries. To inspect an entire object, the laser beam must scan the complete surface of the object. The incident angle of the laser beam will then differ depending on the location on the object that is irradiated. While oblique incidence of the laser beam will excite ultrasonic waves, there is a possibility that these waves will be different from those excited at normal incidence. For the establishment of reliable inspection techniques, a deeper understanding of laser ultrasonic waves is required. In this paper, the generation of ultrasonic waves by lasers at oblique incidence is numerically investigated. An integral expression for the temperature distribution that satisfies the thermal conduction is derived and then finite element method (FEM) simulations of the generated elastic waves are performed. In the case of a small incident angle of the laser beam, the directional dependence of the generated ultrasonic waves is small. However, with a large incident angle, the generated waves exhibit directionality in the wave intensity. Although the incident angle does not need to be considered in the ordinary use of laser ultrasonic devices, the detectability of defects may be affected when the angle is very large.