Simulation using computational methods is well-established for investigating mechanical and haemodynamic properties of blood vessels, however few groups have applied this technology to microvascular anastomoses. This study, for the first time, employs analytic and numeric models of sutured and coupled microarterial anastomoses to evaluate the elastic and failure properties of these techniques in realistic geometries using measured arterial waveforms. Computational geometries were created of pristine microvessels and microarterial anastomoses, performed using sutures and a coupling device. Vessel wall displacement, stress, and strain distributions were predicted for each anastomotic technique using finite element analysis (FEA) software in both static and transient simulations. This study focussed on mechanical properties of the anastomosis immediately after surgery, as failure is most likely in the early post-operative period. Comparisons were also drawn between stress distributions seen in analogous non-compliant simulations. The maximum principal strain in a sutured anastomosis was found to be 84% greater than in a pristine vessel, whereas a mechanically coupled anastomosis reduced arterial strain predictions by approximately 55%. Stress distributions in the sutured anastomoses simulated here differed to those in reported literature. This result is attributed to the use of bonded connections in existing studies, to represent healed surgical sites. This has been confirmed by our study using FEA, and we believe this boundary condition significantly alters the stress distribution, and is less representative of the clinical picture following surgery. We have demonstrated that the inertial effects due to motion of the vessel during pulsatile flow are minimal, since the differences between the transient and static strain calculations range from around 0.6–7% dependent on the geometry. This implies that static structural analyses are likely sufficient to predict anastomotic strains in these simulations. Furthermore, approximations of the shear strain rate (SSR) were calculated and compared to analogous rigid-walled simulations, revealing that wall compliance had little influence on their overall magnitude. It is important to highlight, however, that SSR variations here are taken in isolation, and that changing pressure gradients are likely to produce much greater variation in vessel wall strain values than the influence of fluid flow alone. Hence, a formal fluid-structure interaction (FSI) study would be necessary to ascertain the true relationship.