We consider light trapping by structural resonances in linear periodic arrays of identical high-index dielectric elements. As the basic elements both subwavelength spheres and rods with circular cross section are investigated . When the array is infinite it is known to support bound states in the radiation continuum (BSCs), i.e. structural resonances with infinite life-time embedded into the continuous spectrum of scattering states. Two classes of the BSCs can be identified, namely, topologically and symmetry protected states. In case of arrays of dielectric spheres we show that there is a Bloch guided BSC mode which is stabilized by a topological singularity in space of the resonance coupling strength. We demonstrate numerically that this Bloch BSC can be employed for guiding light pulses above the line of light. If the infinite array is terminated at both ends to form a finite chain of dielectric elements the BSCs become high-Q resonances. We evaluate the asymptotic behavior of the Q-factor of such resonances against the number of elements in the array. We demonstrate numerically that under illumination by a plane wave nite arrays of 10-15 silicon nanospheres can be used to enhance the amplitude of the impinging light at least by order of magnitude in the visible-to-near infrared range when the material and geometrical parameters of the systems are tuned to the structural resonance associated with a BSC.