Wireless powered mobile edge computing (WP-MEC) has been recognized as a promising solution to enhance the computational capability and sustainable energy supply for low-power wireless devices (WDs). However, when the communication links between the hybrid access point (HAP) and WDs are hostile, the energy transfer efficiency and task offloading rate are compromised. To tackle this problem, we propose to employ multiple intelligent reflecting surfaces (IRSs) to WP-MEC networks. Based on the practical IRS phase shift model, we formulate a total computation rate maximization problem by jointly optimizing downlink/uplink IRSs passive beamforming, downlink energy beamforming and uplink multi-user detection (MUD) vector at HAPs, task offloading power and local computing frequency of WDs, and the time slot allocation. Specifically, we first derive the optimal time allocation for downlink wireless energy transmission (WET) to IRSs and the corresponding energy beamforming. Next, with fixed time allocation for the downlink WET to WDs, the original optimization problem can be divided into two independent subproblems. For the WD charging subproblem, the optimal IRSs passive beamforming is derived by utilizing the successive convex approximation (SCA) method and the penalty-based optimization technique, and for the offloading computing subproblem, we propose a joint optimization framework based on the fractional programming (FP) method. Finally, simulation results validate that our proposed optimization method based on the practical phase shift model can achieve a higher total computation rate compared to the baseline schemes.