This paper presents a new principle in wide-band amplifier design. It is shown that, by an appropriate distribution of ordinary electron tubes along artificial transmission lines, it is possible to obtain amplification over much greater bandwidths than would be possible with ordinary circuits. The ordinary concept of "maximum bandwidth-gain product" does not apply to this distributed amplifier. The high-frequency limit of the distributed amplifier appears to be determined by the grid-loading effects. The distributed amplifier provides means for designing amplifiers either of the low-pass or band-pass types. The low-pass amplifiers can be made to have a uniform frequency response from dc to frequencies as high as several hundred Mc using commercially available tubes. The general design considerations included in this paper are: The effect of improper termination of transmission lines; methods for controlling the frequency response and phase characteristic; the design which provides the required gain with fewest possible number of tubes; and a discussion of high-frequency limitations. The noise factor of the amplifier is evaluated. Practical amplifiers, designed according to the principles described in this paper, have been built and have verified the theoretical predictions. Experimental work will be described in a forthcoming paper.