Bispecific monoclonal antibodies (bsmAbs) are expected to provide targeted drug delivery that overcomes the dose-limiting toxicities often accompanying antibody-drug conjugates (ADC) in clinical practice. Much attention has been paid in the past to target selection, mAb affinities and the payload linker design, but challenges remain. Here, we demonstrate, by physiologically based pharmacokinetic (PBPK) in silico modeling and simulation, that the tissue-targeting accuracy of mono- and bispecific antibody therapeutics is substantially limited by normal physiological characteristics like organ volumes, blood flow rates, lymphatic circulation, and rates of extravasation. Only a small fraction of blood flows through solid tumor, where the diffusion-driven extravasation is relatively slow compared with many other organs. EGFR and HER2 are used as model antigens based on their experimentally measured tissue and tumor expression levels, but the approach is generic and can account for the cellular expression variation of targets. The model confirms experimental observations that only about 0.1-1% of the dosed mAb is likely to reach the tumor, while the rest ends up in healthy tissues due to target-mediated internalization and nonspecific uptake. The model suggests that the dual-positive tumor cell targeting specificity with bispecific antibodies is likely to be higher at lower drug concentrations and doses. However, this can be offset by elevated drug exposure in more accessible healthy tissues, primarily endothelium. The balance of exposure can be shifted toward tumor cells by using higher doses, albeit at the expense of more extensive target engagement elsewhere in the body, suggesting the need to adapt the toxicity of the payload if ADCs are considered. We suggest that PBPK modeling can guide and support biologics and bsmAb development, from target evaluation and drug optimization to therapeutic dose selection.