Herein, we report on the mathematical modelling and experimental study of the regime of nonsoliton mode locking in a laser based on the Yb3+:LuAlO3 (Yb:LuAP) crystal with longitudinal pumping by laser diode radiation. Simulation based on the Haus master equation permitted to determine the requirements for the parameters of a saturable absorber (SA), the level of the average output power, the size of the TEM00 mode of the cavity in the active element and on the gate to obtain a stable regime of generation of picosecond laser pulses. Laser experiments were carried out in a fourmirror X-shaped resonator using a semiconductor saturable mirror (SESAM) as a passive modulator and a laser diode with a fiber output of a maximum power up to 30 W at a wavelength of 978.5 nm as a pump source. We obtained a stable passive mode locking with a maximum average output power of up to 12 W and an ultrashort pulse duration of about 2 ps at an optical conversion efficiency of pump radiation into lasing radiation of about 38 %. Laser pulses were obtained at a central wavelength of about 999 nm with a minimum Stokes shift (about 2 %) with respect to the pump radiation, which significantly reduced the thermal load on the active element. Additionally, the preliminary results on the second harmonic generation and synchronous pumping of a parametric light generator using a Yb3+ : LuAlO3 crystal laser as a pump source are presented.