Primary immunodeficiencies (PIDs) are a group of over 300 hereditary, heterogeneous, and mainly rare disorders that affect the immune system. Various aspects of immune system and PID proteins and genes have been investigated and facilitate systems biological studies of effects of PIDs on B cell physiology and response. We reconstructed a B cell network model based on data for the core B cell receptor activation and response processes and performed semi-quantitative dynamic simulations for normal and B cell PID failure modes. The results for several knockout simulations correspond to previously reported molecular studies and reveal novel mechanisms for PIDs. The simulations for CD21, CD40, LYN, MS4A1, ORAI1, PLCG2, PTPRC, and STIM1 indicated profound changes to major transcription factor signaling and to the network. Significant effects were observed also in the BCL10, BLNK, BTK, loss-of-function CARD11, IKKB, MALT1, and NEMO, simulations whereas only minor effects were detected for PIDs that are caused by constitutively active proteins (PI3K, gain-of-function CARD11, KRAS, and NFKBIA). This study revealed the underlying dynamics of PID diseases, confirms previous observations, and identifies novel candidates for PID diagnostics and therapy.