The paper describes a method developed for the indirect cuffless estimation of arterial blood pressure (ABP) from two/three-channel photoplethysmography (PPG) signals. It is important when the actual ABPs cannot be measured, e.g., during scanning inside a magnetic resonance imager. The proposed procedure uses heart pulse transmission parameters (HPTPs) extracted from the second derivative PPG signals. The linear regression method was used to calculate the relation between the determined HPTPs and the ABPs measured in parallel by a blood pressure monitor. The ABP values were estimated by the inverse conversion characteristic calculated from these linear relations. Three auxiliary investigations were performed first to find appropriate settings for PPG signal processing. We tested the accuracy of ABP estimation using two small corpora of multi-channel PPG records sensed during our previous experiments. We also analyzed the distribution of the determined HPTP values depending on the hand and gender for the mapping of a mutual relationship of HPTPs and measured ABPs. The final estimation errors were evaluated graphically (by correlation scatter plots and Bland–Altman plots) and numerically (by a correlation coefficient between the measured and estimated ABPs and by enumeration of the relative estimation error). The obtained results achieve acceptable mean values of −2.6/−3.5 mm Hg for systolic/diastolic ABPs.