We study electron spin relaxation in one-dimensional structures of finite length in the presence of Bychkov-Rashba spin-orbit coupling and boundary spin relaxation. Using a spin kinetic equation approach, we formulate boundary conditions for the case of a partial spin polarization loss at the boundaries. These boundary conditions are used to derive corresponding boundary conditions for spin drift-diffusion equation. The later is solved analytically for the case of relaxation of a homogeneous spin polarization in 1D finite length structures. It is found that the spin relaxation consists of three stages (in some cases, two) -an initial D'yakonov-Perel' relaxation is followed by spin helix formation and its subsequent decay. Analytical expressions for the decay time are found. We support our analytical results by results of Monte Carlo simulations. Dynamics of electron spin polarization in semiconductor structures has attracted a lot of attention recently in the context of spintronics 1-3 , which is playing a fundamental role in the novel technological developments based on different effects in this scientific area. Moreover, the ability to understand and predict the dynamics of electron spins in semiconductors is also important for the area of two terminal electronic devices with memory, so-called memristive devices 4-8 . In some of them 4,6 , the electron spin degree of freedom defines their internal state and, consequently, is responsible for their time-dependent memory response.It has been shown by us recently 9-11 that the system boundaries significantly modify the dynamics of process. For example, we have demonstrated 10 that in finite size 2D systems, the spin polarization density decays much slower than in the bulk and the exponential spin polarization decay rate is defined by both the system size and strength of spin-orbit interaction. In finite length wires 9 and channels 11 (oriented in a specific direction), changes in the electron spin relaxation are even more pronounced: instead of relaxing to zero, the homogeneous electron spin polarization relaxes into a persistent spin polarization structure known as the spin helix 12-15 -a spin polarization configuration in which the direction of spin polarization density rotates along the wire.In real experimental situations, the spin helix configuration can not exist infinitely long. Here, we assume that the main decay mechanism is due to spin relaxation at system boundaries. Indeed, local strong random electric fields in the vicinity of boundaries result in a random spin-orbit interaction influencing the electron spin degree of freedom. It is thus important to develop a theory and model spin relaxation in constrained geometries taking into account the boundary spin relaxation and understand how the boundary spin relaxation changes the overall character of electron spin relaxation in the entire system.In this paper, we use both spin kinetic 11 and diffusion [15][16][17][18][19] equations to investigate the dynamics of electron spin polarization in semiconductor ...