Edentulism (toothlessness) changes dietary habits resulting in obesity, diabetes, and coronary artery disease;​ and, thirty percent of people aged 65-74 years suffer from edentulism, globally. Dental implants, as anchors to replace the natural root of the tooth and support dental prostheses, have become a standard treatment for edentulous patients. Sufficient anchorage (mechanical engagement between bone and implant during insertion) and primary fixation (mechanical engagement under loading) of dental implants have been recommended for positive clinical outcomes. Rigid polyurethane (PU) foam as standard bone surrogate material has been widely used in preclinical studies and dental implant designs. However, the mechanics of anchorage and primary fixation and their relationship for bone surrogate-implant system is not well understood. Two main mechanics dominate anchorage and primary fixation of dental implants:​ thread mechanics and press-fit established by tapered body. Therefore, the objective of this research was to comprehensively investigate effects of implant design such as tapered body on anchorage and primary fixation of dental implants in PU foam combining mechanical experiments, analytical models, and finite element analyses (FEAs). A new analytical model for the insertion torque (IT) was proposed to differentiate contributions of the thread and press-fit mechanics on IT with two parameters:​ effective force, 𝐹′, and effective pressure, 𝑝′. Including the PU foam damage during insertion and under loadings, FEA models for both insertion and primary fixation presented in this study were validated against experimental results. By combining the mechanical testing, analytical modelling and numerical modelling, this research found:​ the dental implant insertion process played a crucial role in primary fixation;​ tapered implants with high insertion press-fit and non-zero 𝑝′ promoted anchorage with high IT, and primary fixation with lower implant motion and higher bone surrogate-implant stiffness under an axial loading compared to parallel-walled implants. These major findings not only contribute a unique dataset to current dental biomechanical field but also provide new findings and assessment methods for anchorage and primary fixation of dental implants. This research work presents new understanding of the mechanics of dental implant anchorage and primary fixation and new methods in support of dental implant design and their preclinical assessment.