The shakedown analysis of printed circuit heat exchangers (PCHEs) is commonly conducted as a significant part of structural integrity assessment. During production and manufacturing, the randomness in structural parameters is unavoidable and can significantly impact the shakedown limit and the structural reliability. However, studies on the influence of random structural parameters are limited due to the expensive computation burden involved. Therefore, this paper aims to achieve efficient stochastic shakedown and reliability analyses of PCHEs with multiple random structural parameters. First, the Linear Matching Method (LMM) is utilized to perform the shakedown analysis of PCHEs. Then, to account for the influence of multiple random structural parameters, the Direct Probability Integral Method (DPIM), as an efficient non-intrusive stochastic analysis method, is introduced. By exploiting the advantages of LMM and DPIM, a novel LMM-DPIM is proposed for the uncertainty qualification analysis of PCHEs. Furthermore, the data-driven neural network model is implemented to improve the computational efficiency of the shakedown simulation procedure. As a result, an LMM-DPIM-based neural network model is established for the efficient stochastic shakedown and reliability analyses of PCHEs. Finally, the high accuracy and efficiency of the proposed model are verified through comparisons with Monte Carlo simulation in the numerical example. Moreover, the results of uncertainty qualification analysis reveal the effects of different random structural parameters on the shakedown limit and reliability of PCHE. Particularly, the fillet radius at the corner of channels has a significant influence on the shakedown limit, and leads to a huge reduction in the structural reliability.